From d8fc5266aefe99ccd5e1f1c0df6a190e56efe828 Mon Sep 17 00:00:00 2001 From: sijanec Date: Sat, 19 Dec 2020 00:13:36 +0100 Subject: =?UTF-8?q?o=C5=A1la?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ang/work/2/dokument.md | 15 + ang/work/3/dokument.md | 12 + mat/advent/8/Makefile | 3 + mat/advent/8/a.out | Bin 0 -> 8440 bytes mat/advent/8/prog.c | 28 + mat/advent/8/vsota | Bin 0 -> 8344 bytes mat/advent/8/vsota.c | 11 + mat/domace_naloge/21/dokument.aux | 33 + mat/domace_naloge/21/dokument.log | 1749 ++++++++++++++++++++++++++++++ mat/domace_naloge/21/dokument.out | 2 + mat/domace_naloge/21/dokument.pdf | Bin 0 -> 63012 bytes mat/domace_naloge/21/dokument.synctex.gz | Bin 0 -> 20556 bytes mat/domace_naloge/21/dokument.tex | 200 ++++ mat/domace_naloge/21/dokument.toc | 4 + mat/domace_naloge/21/stderr.log | 1 + mat/domace_naloge/21/stdout.log | 735 +++++++++++++ nem/delo/1512/dokument.md | 12 + nem/delo/1612/dokument.md | 7 + 18 files changed, 2812 insertions(+) create mode 100644 ang/work/2/dokument.md create mode 100644 ang/work/3/dokument.md create mode 100644 mat/advent/8/Makefile create mode 100755 mat/advent/8/a.out create mode 100644 mat/advent/8/prog.c create mode 100755 mat/advent/8/vsota create mode 100644 mat/advent/8/vsota.c create mode 100644 mat/domace_naloge/21/dokument.aux create mode 100644 mat/domace_naloge/21/dokument.log create mode 100644 mat/domace_naloge/21/dokument.out create mode 100644 mat/domace_naloge/21/dokument.pdf create mode 100644 mat/domace_naloge/21/dokument.synctex.gz create mode 100644 mat/domace_naloge/21/dokument.tex create mode 100644 mat/domace_naloge/21/dokument.toc create mode 100644 mat/domace_naloge/21/stderr.log create mode 100644 mat/domace_naloge/21/stdout.log create mode 100644 nem/delo/1512/dokument.md create mode 100644 nem/delo/1612/dokument.md diff --git a/ang/work/2/dokument.md b/ang/work/2/dokument.md new file mode 100644 index 0000000..80fd42e --- /dev/null +++ b/ang/work/2/dokument.md @@ -0,0 +1,15 @@ +Work +==== + +1. Even if she comes late, ring me when she arrives. +No matter how late she arrives, ring me after. +2. Talented though he is, he can't find a job. +Even though he is talented, he is unable to find a job. +3. In spite of the train strike, she still managed to get to work. +Even though there was a train strike, she managed to get to work. +4. Whatever you say in protest, you can do nothing to change the situation. +No matter what you say in protest, you can do nothing to change the situation. +5. ... +Cold though the lights are, the days are warm. + +Housework: do some stuff, I can't remember what though. diff --git a/ang/work/3/dokument.md b/ang/work/3/dokument.md new file mode 100644 index 0000000..7290d8b --- /dev/null +++ b/ang/work/3/dokument.md @@ -0,0 +1,12 @@ +Adverbial clauses - Practice +============================ + +1. Articulate as she is, she failed to succeed in a negotiation. +2. He puts a lot of effort into his word, however, he hasn't shown any progress yet. +3. Despite her being in a difficult situation, she is always willing to help me. +4. With a view to applying for a job in Italy she is studying Italian. +5. In fear of missing the train, he set the alarm of 6.30. +6. Such boring music made everyone nearly fall asleep. +7. With the aim of buying a new car, she is saving up money. +8. In case the shops were closed, we took a lot of food. +9. She was too tired to participate in our discussion. diff --git a/mat/advent/8/Makefile b/mat/advent/8/Makefile new file mode 100644 index 0000000..ec92f02 --- /dev/null +++ b/mat/advent/8/Makefile @@ -0,0 +1,3 @@ +default: + gcc prog.c + gcc vsota.c -ovsota diff --git a/mat/advent/8/a.out b/mat/advent/8/a.out new file mode 100755 index 0000000..9fea777 Binary files /dev/null and b/mat/advent/8/a.out differ diff --git a/mat/advent/8/prog.c b/mat/advent/8/prog.c new file mode 100644 index 0000000..172cbe0 --- /dev/null +++ b/mat/advent/8/prog.c @@ -0,0 +1,28 @@ +#include +#include +int main (int argc, char ** argv) { + if (argc != 1+3) { + fprintf(stderr, "uporaba: %s \nprimer: %s 1000 9999 8499\n", argv[0], argv[0]); + return 1; + } + unsigned long long int o = strtoull(argv[1], NULL, 10); + unsigned long long int d = strtoull(argv[2], NULL, 10); + unsigned long long int n = strtoull(argv[3], NULL, 10); + unsigned long long int i = o; + unsigned long long int j = o; + unsigned long long int s = 0; + for (i = o; i <= d; i++) { + fprintf(stderr, "\rpreostane še %llu iteracij", n-i); + s = 0; + for (j = o; j <= d; j++) { + if (j == i) + continue; + s += j; + } + if (n * i == s) + break; + } + fprintf(stdout, "\rče seštejemo vsa števila od %llu do %llu, razen %llu, bo\n" + "vsota vseh %llu, kar je %llu*%llu.\n", o, d, i, s, n, i); + return 0; +} diff --git a/mat/advent/8/vsota b/mat/advent/8/vsota new file mode 100755 index 0000000..7581730 Binary files /dev/null and b/mat/advent/8/vsota differ diff --git a/mat/advent/8/vsota.c b/mat/advent/8/vsota.c new file mode 100644 index 0000000..50d4ef6 --- /dev/null +++ b/mat/advent/8/vsota.c @@ -0,0 +1,11 @@ +#include +#include +int main (int argc, char ** argv) { + unsigned long long int a = 0; + unsigned long long int i = 0; + for (i = 1000; i <= 9999; i++) { + a += i; + } + fprintf(stdout, "rezultat vsote je: %llu\n", a); + return 0; +} diff --git a/mat/domace_naloge/21/dokument.aux b/mat/domace_naloge/21/dokument.aux new file 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mode 100644 index 0000000..7416f2f --- /dev/null +++ b/mat/domace_naloge/21/dokument.out @@ -0,0 +1,2 @@ +\BOOKMARK [1][-]{section.1}{Vaje Matematika 2: stran 55, \235tiri naloge 349-361}{}% 1 +\BOOKMARK [1][-]{section.2}{Zakljucek}{}% 2 diff --git a/mat/domace_naloge/21/dokument.pdf b/mat/domace_naloge/21/dokument.pdf new file mode 100644 index 0000000..4425df7 Binary files /dev/null and b/mat/domace_naloge/21/dokument.pdf differ diff --git a/mat/domace_naloge/21/dokument.synctex.gz b/mat/domace_naloge/21/dokument.synctex.gz new file mode 100644 index 0000000..6649dfe Binary files /dev/null and b/mat/domace_naloge/21/dokument.synctex.gz differ diff --git a/mat/domace_naloge/21/dokument.tex b/mat/domace_naloge/21/dokument.tex new file mode 100644 index 0000000..52190a6 --- /dev/null +++ b/mat/domace_naloge/21/dokument.tex @@ -0,0 +1,200 @@ +% !TeX encoding = UTF-8 +% !TeX spellcheck = sl_SI +% do-vimlatex-onwrite +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage{etoolbox} +\usepackage[hidelinks]{hyperref} +\usepackage[a4paper, total={7in, 10in}]{geometry} +\usepackage{graphicx} +\usepackage{hologo} +\usepackage{amssymb} +\usepackage{calculator} +\usepackage{pgfplots} +\usepackage[inline]{enumitem} +\usepackage{siunitx} +\usepackage{multicol} +\usepackage{tabularcalc} +\usepackage{amsmath} +\usepackage{float} +\usepackage{tasks} +\usepackage{filecontents} +\usepackage{textcomp} +\usepackage{tkz-euclide} +\usepackage{dirtytalk} +\usepackage{csquotes} +\usepackage{listings} +\usepackage{datetime} % [ddMMyyyy] +\usepackage{ccicons} +\usepackage{chemformula} +\usepackage{gensymb} +\usepackage[normalem]{ulem} +\usepackage[slovene]{babel} +\usepackage{cancel} +\usepackage{tabularx} +\usepackage{xcolor} +\usepackage{colortbl} +\usepackage{exsheets} +\usepackage{harpoon} +\newcolumntype{Y}{>{\centering\arraybackslash}X} +% \usepackage{multienum} % weird with labels +\usetikzlibrary{calc} %% not really needed............. idk. +%\usetikzlibrary{external} +% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (: +%\tikzexternalize +\sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol +\newcommand\ddfrac[2]{\frac{\displaystyle #1}{\displaystyle #2}} +\newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development +\newcommand{\razhroscevanje}{1} +\definecolor{codegreen}{rgb}{0,0.6,0} +\definecolor{codered}{rgb}{1,0,0} +\definecolor{codegray}{rgb}{0.5,0.5,0.5} +\definecolor{codepurple}{rgb}{0.58,0,0.82} +\definecolor{backcolour}{rgb}{0.95,0.95,0.92} +\renewcommand{\dateseparator}{. } +\settimeformat{hhmmsstime} +\lstdefinestyle{mystyle}{ + backgroundcolor=\color{backcolour}, + commentstyle=\color{codegreen}, + keywordstyle=\color{magenta}, + numberstyle=\tiny\color{codegray}, + stringstyle=\color{codepurple}, + basicstyle=\ttfamily\footnotesize, + breakatwhitespace=false, + breaklines=true, + captionpos=b, + keepspaces=true, + numbers=left, + numbersep=5pt, + showspaces=false, + showstringspaces=false, + showtabs=false, + tabsize=2 +} +\lstset{style=mystyle} +\def\@maketitle{% + \newpage + \null + \vskip 2em% + \begin{center}% + \let \footnote \thanks + {\LARGE \@title \par}% + \vskip 1.5em% + {\large + \lineskip .5em% + \begin{tabular}[t]{c}% <------ + \@author% <------ Authors + \end{tabular}\par}% <------ + \vskip 1em% + {\large \@date}% + \end{center}% + \par + \vskip 1.5em} +%opening +\newcommand{\snovdn}{Linearna kombinacija vektorjev, baza } +\newcommand{\predmdn}{mat} +\newcommand{\predmkaj}{domace\_naloge} +\newcommand{\stevilkadn}{21} +\newcommand{\cm}[1]{\SI{#1}{\centi\meter}} +\newcommand{\kmh}[1]{\SI{#1}{\kilo\meter\per\hour}} +\makeatletter +\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname} +\newcommand{\@xslalph}[1]{% + \ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i% + \or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}% + \or t\or u\or v\or z\or \v{z} + \else\@ctrerr\fi% +} +\AddEnumerateCounter{\xslalph}{\@xslalph}{m} +\makeatother +\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma +\newcommand*\textfrac[2]{ + \frac{\text{#1}}{\text{#2}} +} +\NewTasks[counter-format=\xslalph*),label-format=\bfseries]{primerTasks}(3) +\newcommand\vektor{\overrightarrow} +\newcommand{\iic}{I\textsuperscript{2}C } +\title{% + \snovdn --- \stevilkadn. domača naloga + \\ + \large Matematika, Gimnazija Bežigrad} +\author{\begin{tabular}{rl} + \textbf{Profesor:} & prof. Vilko Domajnko\\ + \textbf{Avtor:} & Anton Luka Šijanec, 2. a +% \textbf{Avtor:} & Anton Luka Šijanec \\ & Member 2 \\ & Member 3 +\end{tabular}} +\newcommand\hcancel[2][black]{\setbox0=\hbox{$#2$}% +\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2} +% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260 +\begin{document} +\maketitle +\begin{abstract} +Ta dokument vsebuje domačo nalogo, ki zajema snov \textit{\snovdn}pri matematiki, in njene rešitve, ki sem jih spisal sam. Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbral naključno. +\end{abstract} +\tableofcontents +\section{Vaje \textit{Matematika 2}: stran 55, štiri naloge 349-361} +\begin{enumerate}[label=\textbf{\arabic*.}] % 350 360 353 352 + \setcounter{enumi}{349} + \item Naj bodo vektorji $\Vec{a}$, $\Vec{b}$ in $\Vec{c}$ bazni vektorji v + prostoru. Vektorja $\Vec{m}$ in $\Vec{n}$ sta enaka + $\Vec{m}=-2\Vec{a}+\frac{3}{2}\Vec{b}+\Vec{c}$ in + $\Vec{n}=-\frac{1}{2}\Vec{a}+\Vec{b}+2\Vec{c}$. + Vektor $2\Vec{m}-\Vec{n}$ zapiši v dani bazi. % 350 + \setcoutner{enumi}{351} + \item Točke $A$, $B$, $C$, $D$ in $E$ ležijo na premici tako, da je + $|AB|:|BC|:|CD|:|DE|=3:2:1:3$. Točki $B$ in $D$ ležita med $A$ in $C$. točka $D$ pa med $B$ in $E$. Naj bo vektor $\Vec{a}=\vektor{BE}$ bazni vektor. Z vektorjem $\Vec{a}$ izrazi vektorje $\vektor{DC}$, $\vektor{AC}$ in $\vektor{DE}$. % 352 + \item Točka $M$ je razpolovišče daljice $CD$ pravokotnika $ABCD$, vektorja + $\Vec{a}=\vektor{AB}$ in $\Vec{b}=\vektor{AD}$ sta bazna vektorja. Z $\Vec{a}$ in $\Vec{b}$ izrazi $\vektor{AC}$, $\vektor{AM}$, $\vektor{BM}$ in $\vektor{MB}$. % 353 + \setcounter{enumi}{359} + \item % 360 + \begin{multicols}{2} + Na stranicah paralelograma $ABCD$ so dane točke $I$, $J$ in $K$, tako + da je $|DI|=|IJ|=|JC|$ in $|BK|=|KC|$. Točka $L$ je razpolovišče daljico $AI$, točka $M$ pa razpolovišče daljice $LJ$. + \begin{enumerate}[label=\textbf{\xslalph*)}] + \item Dana sta vektorja $\vektor{AB}=\Vec{a}$ in $\vektor{BC}=\Vec{b}$. + Izrazi vektor $\vektor{MK}$ z vektorjema $\Vec{a}$ in $\Vec{b}$. + \item Naj bosta bazna vektorja $\vektor{LI}=\Vec{u}$ in + $\vektor{LM}=\Vec{v}$. Izrazi vektorja $\vektor{AD}$ in $\vektor{AB}$ + z vektorjema $\Vec{u}$ in $\Vec{v}$. + \end{enumerate} + \vfill\null\columnbreak + \begin{tikzpicture}[scale=2] + \tkzDefPoint(1,2){D} + \tkzDefPoint(2,2){I} + \tkzDefPoint(3,2){J} + \tkzDefPoint(4,2){C} + \tkzDefPoint(1,1){L} + \tkzDefPoint(2,1.5){M} + \tkzDefPoint(3.5,1){K} + \tkzDefPoint(0,0){A} + \tkzDefPoint(3,0){B} + \tkzDrawPolygon[red](A,B,C,D) + \tkzDrawLine[blue, add = 0 and 0](A,I) + \tkzDrawLine[blue, add = 0 and 0](L,J) + \tkzDrawLine[blue, add = 0 and 0](M,K) + \tkzDrawPoints(D,I,J,C,L,M,K,A,B) + \tkzLabelPoints(D,I,J,C,L,M,K,A,B) + \end{tikzpicture} + \end{multicols} +\end{enumerate} + + +\section{Zaključek} +Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in +\hologo{LaTeX}\footnote{Za izdelavo dokumenta potrebujete \texttt{TeXLive 2020}.} +izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo v mojem šolskem Git repozitoriju na +\url{https://git.sijanec.eu/sijanec/sola-gimb-2} v mapi +\href{https://git.sijanec/sola-gimb-2/src/branch/master/\predmdn/\predmkaj/\stevilkadn/}{/\predmdn/\predmkaj/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/\predmkaj/\stevilkadn/dokument.pdf} in/ali \url{https://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/master/\predmdn/\predmkaj/\stevilkadn/dokument.pdf}. + +\if\razhroscevanje1 +\section*{Razhroščevalne informacije} +Te informacije so generirane, ker je omogočeno razhroščevanje. Pred objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroscevanje} na 0 v začetku dokumenta. + +Grafi imajo natančnost \functionSamples\space točk na graf. + +Konec generiranja dokumenta: \today\ ob \currenttime\footnote{To ne nakazuje dejanskega časa, ko je bil dokument napisan, temveč čas, ko je bi dokument generiran v PDF/DVI obliko. Isto velja za datum v glavi dokumenta. Če berete direktno iz LaTeX datoteke, bo to vedno današnji datum.}%\input|"date -Ins" + +Dokument se je generiral R0qK1KR2 \SI{}{\second}. +\fi +% \item $$$$ aaasecgeninsaaa R0qK1KR2 +\end{document} diff --git a/mat/domace_naloge/21/dokument.toc b/mat/domace_naloge/21/dokument.toc new file mode 100644 index 0000000..3358445 --- /dev/null +++ b/mat/domace_naloge/21/dokument.toc @@ -0,0 +1,4 @@ +\babel@toc {slovene}{} +\babel@toc {slovene}{} +\contentsline {section}{\numberline {1}Vaje \textit {Matematika 2}: stran 55, štiri naloge 349-361}{1}{section.1}% +\contentsline {section}{\numberline {2}Zaključek}{1}{section.2}% diff --git a/mat/domace_naloge/21/stderr.log b/mat/domace_naloge/21/stderr.log new file mode 100644 index 0000000..7464410 --- /dev/null +++ b/mat/domace_naloge/21/stderr.log @@ -0,0 +1 @@ +<<75F40139103067DB4935B23B6287835A>]/Index[ 0 143]/Info 141 0 R/Length 369/Root 140 0 R/Size 143/W[ 1 3 1]>> diff --git a/mat/domace_naloge/21/stdout.log 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This may have been caused + **** by a problem while converting or transfering the file. + **** Ghostscript will attempt to recover the data. + **** However, the output may be incorrect. + **** Error: stream Length incorrect. + Output may be incorrect. diff --git a/nem/delo/1512/dokument.md b/nem/delo/1512/dokument.md new file mode 100644 index 0000000..daad710 --- /dev/null +++ b/nem/delo/1512/dokument.md @@ -0,0 +1,12 @@ +Ordinalzahlen +============= + +* vom bis zum +* vom zwanzigsten bis zum dreiundzwanzigsten +* der dritte Januar +* Was macht man zu Weihnachten +* backt man eine Torte +* lädt + + +HG:/122/123 diff --git a/nem/delo/1612/dokument.md b/nem/delo/1612/dokument.md new file mode 100644 index 0000000..f16110f --- /dev/null +++ b/nem/delo/1612/dokument.md @@ -0,0 +1,7 @@ +Termine, Termine, ... +===================== + +* den Termin absagen oder verschieben - odpovedati ali prestaviti +* Sie möchte den Termin auf 21. 8. um 15.00 verschieben. +* einen Termin vereinbaren, 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[(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(AB)]TJ/F14 9.9626 Tf 15.528 0 Td [(j)]TJ/F8 9.9626 Tf 6.091 0 Td [(:)]TJ/F14 9.9626 Tf 6.091 0 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(B)-50(C)]TJ/F14 9.9626 Tf 15.89 0 Td [(j)]TJ/F8 9.9626 Tf 6.09 0 Td [(:)]TJ/F14 9.9626 Tf 6.091 0 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(C)-72(D)]TJ/F14 9.9626 Tf 16.358 0 Td [(j)]TJ/F8 9.9626 Tf 6.091 0 Td [(:)]TJ/F14 9.9626 Tf 6.09 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(D)-28(E)]TJ/F14 9.9626 Tf 16.453 0 Td [(j)]TJ/F8 9.9626 Tf 6.091 0 Td [(=)-334(3)-333(:)-334(2)-333(:)-334(1)-333(:)-334(3.)-545(T)84(o)27(\024)473(cki)]TJ/F11 9.9626 Tf 94.888 0 Td [(B)]TJ/F8 9.9626 Tf 11.711 0 Td [(in)]TJ/F11 9.9626 Tf 11.957 0 Td [(D)]TJ/F8 9.9626 Tf -470.569 -13.95 Td [(le)28(\024)472(zita)-296(med)]TJ/F11 9.9626 Tf 47.406 0 Td [(A)]TJ/F8 9.9626 Tf 10.42 0 Td [(in)]TJ/F11 9.9626 Tf 11.249 0 Td [(C)]TJ/F8 9.9626 Tf 7.833 0 Td [(.)-432(to)28(\024)472(ck)56(a)]TJ/F11 9.9626 Tf 32.988 0 Td [(D)]TJ/F8 9.9626 Tf 11.472 0 Td [(pa)-296(med)]TJ/F11 9.9626 Tf 34.676 0 Td [(B)]TJ/F8 9.9626 Tf 11.004 0 Td [(in)]TJ/F11 9.9626 Tf 11.25 0 Td [(E)]TJ/F8 9.9626 Tf 7.929 0 Td [(.)-432(Na)-55(j)-296(b)-28(o)-296(v)28(ektor)]TJ/F11 9.9626 Tf 69.558 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.657 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 6.808 Td [(\000)476(\000)475(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(E)]TJ/F8 9.9626 Tf 18.933 0 Td [(bazni)-296(v)28(ektor.)-432(Z)-296(v)28(ektorjem)]TJ/F11 9.9626 Tf 115.247 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.837 0 Td [(izrazi)-296(v)28(ektorje)]TJ/F14 9.9626 Tf -417.975 -6.589 Td [(\000)457(\000)457(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(D)-28(C)]TJ/F8 9.9626 Tf 16.358 0 Td [(,)]TJ/F14 9.9626 Tf 6.089 6.807 Td [(\000)242(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AC)]TJ/F8 9.9626 Tf 18.626 0 Td [(in)]TJ/F14 9.9626 Tf 11.623 6.807 Td [(\000)452(\000)452(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(D)-28(E)]TJ/F8 9.9626 Tf 16.453 0 Td [(.)]TJ/F14 9.9626 Tf 99.708 -9.286 Td [(\000)457(\000)457(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(D)-28(C)]TJ/F8 9.9626 Tf 19.126 0 Td [(=)]TJ 11.711 6.74 Td [(1)]TJ +ET +q +1 0 0 1 270.238 348.832 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 270.238 339.507 Td [(4)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F8 9.9626 Tf 5.89 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.808 Td [(\000)242(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AC)]TJ/F8 9.9626 Tf 18.072 0 Td [(=)]TJ 11.712 6.74 Td [(5)]TJ +ET +q +1 0 0 1 319.214 348.832 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 319.214 339.507 Td [(3)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F8 9.9626 Tf 5.89 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.808 Td [(\000)452(\000)452(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(D)-28(E)]TJ/F8 9.9626 Tf 19.22 0 Td [(=)]TJ 11.712 6.74 Td [(3)]TJ +ET +q +1 0 0 1 369.338 348.832 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 369.338 339.507 Td [(4)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ +0 g 0 G +/F77 9.9626 Tf -329.696 -28.256 Td [(353.)]TJ +0 g 0 G +/F8 9.9626 Tf 25.349 0 Td [(T)83(o)28(\024)472(ck)56(a)]TJ/F11 9.9626 Tf 28.918 0 Td [(M)]TJ/F8 9.9626 Tf 14.209 0 Td [(je)-347(razp)-28(olo)28(vi)53(\024)447(s)28(\024)472(ce)-347(daljice)]TJ/F11 9.9626 Tf 98.183 0 Td [(C)-72(D)]TJ/F8 9.9626 Tf 19.816 0 Td [(pra)28(v)28(ok)27(otni)1(k)55(a)]TJ/F11 9.9626 Tf 59.387 0 Td [(AB)-50(C)-72(D)]TJ/F8 9.9626 Tf 31.886 0 Td [(,)-351(v)28(ektorja)]TJ/F11 9.9626 Tf 44.544 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.885 0 Td [(=)]TJ/F14 9.9626 Tf 10.744 6.808 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AB)]TJ/F8 9.9626 Tf 18.987 0 Td [(in)]TJ/F11 9.9626 Tf 10.641 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 7.271 0 Td [(=)]TJ/F14 9.9626 Tf 10.744 6.808 Td [(\000)475(\000)475(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AD)]TJ/F8 9.9626 Tf 19.454 0 Td [(sta)-347(bazna)-347(v)28(ektorja.)-486(Z)]TJ/F11 9.9626 Tf -385.411 -13.396 Td [(~)437(a)]TJ/F8 9.9626 Tf 9.21 0 Td [(in)]TJ/F11 9.9626 Tf 10.504 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 7.597 0 Td [(izrazi)]TJ/F14 9.9626 Tf 26.595 6.808 Td [(\000)242(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AC)]TJ/F8 9.9626 Tf 15.305 0 Td [(,)]TJ/F14 9.9626 Tf 6.088 6.808 Td [(\000)363(\000)363(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AM)]TJ/F8 9.9626 Tf 18.223 0 Td [(,)]TJ/F14 9.9626 Tf 6.089 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(M)]TJ/F8 9.9626 Tf 22.129 0 Td [(in)]TJ/F14 9.9626 Tf 11.623 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(B)]TJ/F8 9.9626 Tf 18.808 0 Td [(.)]TJ/F14 9.9626 Tf -48.295 -19.248 Td [(\000)242(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AC)]TJ/F8 9.9626 Tf 18.072 0 Td [(=)]TJ/F11 9.9626 Tf 9.892 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.808 Td [(\000)363(\000)363(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AM)]TJ/F8 9.9626 Tf 20.991 0 Td [(=)]TJ 11.711 6.74 Td [(1)]TJ +ET +q +1 0 0 1 265.673 281.124 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 265.673 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(M)]TJ/F8 9.9626 Tf 21.575 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(\000)]TJ/F8 9.9626 Tf 8.945 6.74 Td [(1)]TJ +ET +q +1 0 0 1 342.353 281.124 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 342.353 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.843 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(;)]TJ/F14 9.9626 Tf 7.748 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(B)]TJ/F8 9.9626 Tf 21.576 0 Td [(=)]TJ 11.711 6.74 Td [(1)]TJ +ET +q +1 0 0 1 411.283 281.124 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 411.283 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F14 9.9626 Tf 8.104 0 Td [(\000)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ +0 g 0 G +/F77 9.9626 Tf -393.983 -23.91 Td [(360.)]TJ +0 g 0 G +/F8 9.9626 Tf 25.349 0 Td [(Na)-279(strani)1(c)-1(ah)-278(paralelograma)]TJ/F11 9.9626 Tf 122.203 0 Td [(AB)-50(C)-72(D)]TJ/F8 9.9626 Tf 34.661 0 Td [(so)-279(dane)-278(to)28(\024)472(ck)28(e)]TJ/F11 9.9626 Tf 60.407 0 Td [(I)]TJ/F8 9.9626 Tf 5.161 0 Td [(,)]TJ/F11 9.9626 Tf 5.651 0 Td [(J)]TJ/F8 9.9626 Tf -228.083 -11.956 Td [(in)]TJ/F11 9.9626 Tf 11.727 0 Td [(K)]TJ/F8 9.9626 Tf 9.174 0 Td [(,)-346(tak)27(o)-343(da)-344(je)]TJ/F14 9.9626 Tf 53.299 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(D)-28(I)]TJ/F14 9.9626 Tf 13.686 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(I)-78(J)]TJ/F14 9.9626 Tf 11.644 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(J)-96(C)]TJ/F14 9.9626 Tf 14.315 0 Td [(j)]TJ/F8 9.9626 Tf 6.193 0 Td [(in)]TJ/F14 9.9626 Tf 11.726 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(B)-50(K)]TJ/F14 9.9626 Tf 17.23 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(K)-72(C)]TJ/F14 9.9626 Tf 17.007 0 Td [(j)]TJ/F8 9.9626 Tf 2.767 0 Td [(.)]TJ -231.798 -11.955 Td [(T)83(o)28(\024)472(ck)56(a)]TJ/F11 9.9626 Tf 28.442 0 Td [(L)]TJ/F8 9.9626 Tf 9.761 0 Td [(je)-299(razp)-28(olo)28(vi)53(\024)447(s)28(\024)472(ce)-300(dalj)1(ico)]TJ/F11 9.9626 Tf 97.307 0 Td [(AI)]TJ/F8 9.9626 Tf 12.633 0 Td [(,)-306(to)28(\024)472(ck)55(a)]TJ/F11 9.9626 Tf 31.768 0 Td [(M)]TJ/F8 9.9626 Tf 13.732 0 Td [(pa)-299(razp)-28(o-)]TJ -193.643 -11.955 Td [(lo)28(vi)53(\024)447(s)28(\024)472(ce)-334(daljice)]TJ/F11 9.9626 Tf 62.876 0 Td [(LJ)]TJ/F8 9.9626 Tf 13.263 0 Td [(.)]TJ +0 g 0 G +/F77 9.9626 Tf -69.227 -19.422 Td [(a\051)]TJ +0 g 0 G +/F8 9.9626 Tf 15.006 0 Td [(Dana)-454(sta)-453(v)28(ektorja)]TJ/F14 9.9626 Tf 84.901 6.808 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AB)]TJ/F8 9.9626 Tf 20.292 0 Td [(=)]TJ/F11 9.9626 Tf 11.889 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 10.409 0 Td [(in)]TJ/F14 9.9626 Tf 12.821 6.808 Td [(\000)480(\000)481(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(C)]TJ/F8 9.9626 Tf 20.654 0 Td [(=)]TJ/F11 9.9626 Tf 11.394 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(.)-805(Izrazi)]TJ -177.754 -13.949 Td [(v)28(ektor)]TJ/F14 9.9626 Tf 30.746 6.807 Td [(\000)278(\000)278(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(M)-109(K)]TJ/F8 9.9626 Tf 23.246 0 Td [(z)-333(v)27(ektorjema)]TJ/F11 9.9626 Tf 58.627 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 9.21 0 Td [(in)]TJ/F11 9.9626 Tf 10.504 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(.)]TJ/F14 9.9626 Tf -67.624 -14.387 Td [(\000)278(\000)278(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(K)]TJ/F8 9.9626 Tf 22.693 0 Td [(=)]TJ 11.712 6.74 Td [(7)]TJ +ET +q +1 0 0 1 196.971 166.782 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 196.971 157.457 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F14 9.9626 Tf 8.104 0 Td [(\000)]TJ/F8 9.9626 Tf 11.158 6.74 Td [(1)]TJ +ET +q +1 0 0 1 221.786 166.782 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 221.786 157.457 Td [(4)]TJ/F11 9.9626 Tf 5.057 9.463 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(;)]TJ +0 g 0 G +/F77 9.9626 Tf -155.578 -24.414 Td [(b\051)]TJ +0 g 0 G +/F8 9.9626 Tf 15.802 0 Td [(Na)-56(j)-445(b)-28(osta)-446(bazna)-445(v)27(ektorja)]TJ/F14 9.9626 Tf 118.303 6.808 Td [(\000)579(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(LI)]TJ/F8 9.9626 Tf 16.575 0 Td [(=)]TJ/F11 9.9626 Tf 12.253 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 10.273 0 Td [(in)]TJ/F14 9.9626 Tf 12.742 6.808 Td [(\000)398(\000)398(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(LM)]TJ/F8 9.9626 Tf 22.165 0 Td [(=)]TJ/F11 9.9626 Tf 11.996 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.573 0 Td [(.)]TJ -209.88 -13.949 Td 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Jones +%Copyright: Copyright (c) 1997, 2009 American Mathematical Society +%Copyright: (), with Reserved Font Name CMR12. +% This Font Software is licensed under the SIL Open Font License, Version 1.1. +% This license is in the accompanying file OFL.txt, and is also +% available with a FAQ at: http://scripts.sil.org/OFL. +%%EndComments +FontDirectory/CMR12 known{/CMR12 findfont dup/UniqueID known{dup +/UniqueID get 5000794 eq exch/FontType get 1 eq and}{pop false}ifelse +{save true}{false}ifelse}{false}ifelse +11 dict begin +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def +/FontName /RLYLLI+CMR12 def +/FontBBox {-34 -251 988 750 }readonly def +/PaintType 0 def +/FontInfo 9 dict dup begin +/version (003.002) readonly def +/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR12.) readonly def +/FullName (CMR12) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 66 /B put +dup 68 /D put +dup 71 /G put +dup 76 /L put +dup 77 /M put +dup 83 /S put +dup 86 /V put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 20 /caron put +dup 44 /comma put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 46 /period put +dup 114 /r put +dup 116 /t put +dup 50 /two put +dup 117 /u put +dup 122 /z put +dup 48 /zero put +readonly def +currentdict end +currentfile eexec +oc;jAw-=%W)-{ru)rAE(@{빴Q|_R +ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ +}3{Z2zݬT2s$Z&{BJ{r̗m1l(zNRr^&%:(/IߺHm!4JxI7bs,OiOl75R 9z(X*Rhn5&g\c9`EgwT!xIJz҈v*lcoƿsdm^%=谺D +u9#3P _] )w +UA8 HuG:DJ(W;]-0<.gSB NlZOLӡ5^9:K*|F +{É ڇE,q>j0^x떲Q'X酉i ;yZPt>p1SV}:ުad0h{JA)Θ[ U=y5pRU&0'-8tIAx*̣$!gRHS;RVU?!lM٬2gO.T7wϓ)?CߠVb7^kJ;c +N* ٍG|Ucͮߢɨl6h6[ 2ߵПZvUlP|%)VǸm׫=&a +Js_̲y|{R6ĴʗB7jIȘ2a% @74 @4(.= `h'p+xvX}?G3D:^ӟ*&4prx5e^hk@S_̎Cl^^}ڶ-q9@e @|wMrc9P(TkruY@MnuW`%?Q8wG3g; dlo 2 Uu6C֋%YT'Rjo1Mn}L+:O/`@ӟӎ4J +B $YaհH Ag0IQ<;v|<6G@tqX>ɏpI%(Xv7}19lAKڮ6]+l_6'3`k*T (]65R-[(EAJ!3s:e*Aܣ ZEsNьmcЪ..> ˆ>Q&x̹znkCfqW-ٕ6qo*p+.gjlZrht?3:2ty&F!w^9vӐy*'ImtӮ:dN#LaRx!d!R *9SDdkb$Vdž^t4}h5eHNrHI,O6'l +NO#xa OTV-(!JZyX !]z@. 5-DL5_rHqg/r秂gͯP%x d꿖xAcŘʺϡYd(*:od`AMPb-nt]#lg&eb5d*OE 5 UThlv9_)$pC+(M ռPVOptcC`ՠ0IJ85YA('针1J ) =n?Epaq\')_4}KY+d>^cV60EZt,)ie Oӟ5ni8B5*Ƅxn@EDP>e$I^na Y>k#w?p͓t!_1 dr{d ,@]+ضCzn{0RUK,&Ձ\ƭТ1LB#Jp0 XJK7ZLD"afI1?jt'8:/(IGʵ6 <+r xj=9zI!ƶreGNXNpA4Us]b;g-L:/ڮpaؖ:1xǔ`V&EE?c CۗǙ77-`$Mv|&sČ 6X!g#ndχ[w䄁n(dَoo_o2<ݻ  xMI^ +[$dDTZ jķi|O.E9wbSsBz֚ȴ!2g6bcrۑW1A"nX14nKOC-NA=9g5=W^x(xڞEt8}NIDʄ!"]}FET2mRi< r3a0!fS&W{V_ ħ/Wc + 15y8/ V㯧٧򁂝*^F}#? 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-6.808 Td [(AD)]TJ/F8 9.9626 Tf 19.454 0 Td [(sta)-347(bazna)-347(v)28(ektorja.)-486(Z)]TJ/F11 9.9626 Tf -385.411 -13.396 Td [(~)437(a)]TJ/F8 9.9626 Tf 9.21 0 Td [(in)]TJ/F11 9.9626 Tf 10.504 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 7.597 0 Td [(izrazi)]TJ/F14 9.9626 Tf 26.595 6.808 Td [(\000)242(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AC)]TJ/F8 9.9626 Tf 15.305 0 Td [(,)]TJ/F14 9.9626 Tf 6.088 6.808 Td [(\000)363(\000)363(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AM)]TJ/F8 9.9626 Tf 18.223 0 Td [(,)]TJ/F14 9.9626 Tf 6.089 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(M)]TJ/F8 9.9626 Tf 22.129 0 Td [(in)]TJ/F14 9.9626 Tf 11.623 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(B)]TJ/F8 9.9626 Tf 18.808 0 Td [(.)]TJ/F14 9.9626 Tf -48.295 -19.248 Td [(\000)242(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AC)]TJ/F8 9.9626 Tf 18.072 0 Td [(=)]TJ/F11 9.9626 Tf 9.892 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.808 Td [(\000)363(\000)363(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AM)]TJ/F8 9.9626 Tf 20.991 0 Td [(=)]TJ 11.711 6.74 Td [(1)]TJ +ET +q +1 0 0 1 265.673 281.124 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 265.673 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(M)]TJ/F8 9.9626 Tf 21.575 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(\000)]TJ/F8 9.9626 Tf 8.945 6.74 Td [(1)]TJ +ET +q +1 0 0 1 342.353 281.124 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 342.353 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.843 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(;)]TJ/F14 9.9626 Tf 7.748 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(B)]TJ/F8 9.9626 Tf 21.576 0 Td [(=)]TJ 11.711 6.74 Td [(1)]TJ +ET +q +1 0 0 1 411.283 281.124 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 411.283 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F14 9.9626 Tf 8.104 0 Td [(\000)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ +0 g 0 G +/F77 9.9626 Tf -393.983 -23.91 Td [(360.)]TJ +0 g 0 G +/F8 9.9626 Tf 25.349 0 Td [(Na)-279(strani)1(c)-1(ah)-278(paralelograma)]TJ/F11 9.9626 Tf 122.203 0 Td [(AB)-50(C)-72(D)]TJ/F8 9.9626 Tf 34.661 0 Td [(so)-279(dane)-278(to)28(\024)472(ck)28(e)]TJ/F11 9.9626 Tf 60.407 0 Td [(I)]TJ/F8 9.9626 Tf 5.161 0 Td [(,)]TJ/F11 9.9626 Tf 5.651 0 Td [(J)]TJ/F8 9.9626 Tf -228.083 -11.956 Td [(in)]TJ/F11 9.9626 Tf 11.727 0 Td [(K)]TJ/F8 9.9626 Tf 9.174 0 Td [(,)-346(tak)27(o)-343(da)-344(je)]TJ/F14 9.9626 Tf 53.299 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(D)-28(I)]TJ/F14 9.9626 Tf 13.686 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(I)-78(J)]TJ/F14 9.9626 Tf 11.644 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(J)-96(C)]TJ/F14 9.9626 Tf 14.315 0 Td [(j)]TJ/F8 9.9626 Tf 6.193 0 Td [(in)]TJ/F14 9.9626 Tf 11.726 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(B)-50(K)]TJ/F14 9.9626 Tf 17.23 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(K)-72(C)]TJ/F14 9.9626 Tf 17.007 0 Td [(j)]TJ/F8 9.9626 Tf 2.767 0 Td [(.)]TJ -231.798 -11.955 Td [(T)83(o)28(\024)472(ck)56(a)]TJ/F11 9.9626 Tf 28.442 0 Td [(L)]TJ/F8 9.9626 Tf 9.761 0 Td [(je)-299(razp)-28(olo)28(vi)53(\024)447(s)28(\024)472(ce)-300(dalj)1(ico)]TJ/F11 9.9626 Tf 97.307 0 Td [(AI)]TJ/F8 9.9626 Tf 12.633 0 Td [(,)-306(to)28(\024)472(ck)55(a)]TJ/F11 9.9626 Tf 31.768 0 Td [(M)]TJ/F8 9.9626 Tf 13.732 0 Td [(pa)-299(razp)-28(o-)]TJ -193.643 -11.955 Td [(lo)28(vi)53(\024)447(s)28(\024)472(ce)-334(daljice)]TJ/F11 9.9626 Tf 62.876 0 Td [(LJ)]TJ/F8 9.9626 Tf 13.263 0 Td [(.)]TJ +0 g 0 G +/F77 9.9626 Tf -69.227 -19.422 Td [(a\051)]TJ +0 g 0 G +/F8 9.9626 Tf 15.006 0 Td [(Dana)-454(sta)-453(v)28(ektorja)]TJ/F14 9.9626 Tf 84.901 6.808 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AB)]TJ/F8 9.9626 Tf 20.292 0 Td [(=)]TJ/F11 9.9626 Tf 11.889 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 10.409 0 Td [(in)]TJ/F14 9.9626 Tf 12.821 6.808 Td [(\000)480(\000)481(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(C)]TJ/F8 9.9626 Tf 20.654 0 Td [(=)]TJ/F11 9.9626 Tf 11.394 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(.)-805(Izrazi)]TJ -177.754 -13.949 Td [(v)28(ektor)]TJ/F14 9.9626 Tf 30.746 6.807 Td [(\000)278(\000)278(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(M)-109(K)]TJ/F8 9.9626 Tf 23.246 0 Td [(z)-333(v)27(ektorjema)]TJ/F11 9.9626 Tf 58.627 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 9.21 0 Td [(in)]TJ/F11 9.9626 Tf 10.504 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(.)]TJ/F14 9.9626 Tf -67.624 -14.387 Td [(\000)278(\000)278(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(K)]TJ/F8 9.9626 Tf 22.693 0 Td [(=)]TJ 11.712 6.74 Td [(7)]TJ +ET +q +1 0 0 1 196.971 166.782 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 196.971 157.457 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F14 9.9626 Tf 8.104 0 Td [(\000)]TJ/F8 9.9626 Tf 11.158 6.74 Td [(1)]TJ +ET +q +1 0 0 1 221.786 166.782 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 221.786 157.457 Td [(4)]TJ/F11 9.9626 Tf 5.057 9.463 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(;)]TJ +0 g 0 G +/F77 9.9626 Tf -155.578 -24.414 Td [(b\051)]TJ +0 g 0 G +/F8 9.9626 Tf 15.802 0 Td [(Na)-56(j)-445(b)-28(osta)-446(bazna)-445(v)27(ektorja)]TJ/F14 9.9626 Tf 118.303 6.808 Td [(\000)579(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(LI)]TJ/F8 9.9626 Tf 16.575 0 Td [(=)]TJ/F11 9.9626 Tf 12.253 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 10.273 0 Td [(in)]TJ/F14 9.9626 Tf 12.742 6.808 Td [(\000)398(\000)398(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(LM)]TJ/F8 9.9626 Tf 22.165 0 Td [(=)]TJ/F11 9.9626 Tf 11.996 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.573 0 Td [(.)]TJ -209.88 -13.949 Td [(Izrazi)-333(v)27(ektorja)]TJ/F14 9.9626 Tf 66.197 6.807 Td [(\000)475(\000)475(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AD)]TJ/F8 9.9626 Tf 19.317 0 Td [(in)]TJ/F14 9.9626 Tf 11.623 6.807 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AB)]TJ/F8 9.9626 Tf 18.85 0 Td [(z)-333(v)27(ektorjema)]TJ/F11 9.9626 Tf 59.122 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 9.152 0 Td [(in)]TJ/F11 9.9626 Tf 11.236 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.574 0 Td [(.)]TJ/F14 9.9626 Tf -164.571 -11.69 Td [(\000)475(\000)475(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AD)]TJ/F8 9.9626 Tf 18.764 0 Td [(=)-278(3)]TJ/F11 9.9626 Tf 15.369 0 Td [(~)487(u)]TJ/F14 9.9626 Tf 8.046 0 Td [(\000)]TJ/F8 9.9626 Tf 9.963 0 Td [(2)]TJ/F11 9.9626 Tf 4.594 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.573 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.807 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AB)]TJ/F8 9.9626 Tf 18.296 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(3)]TJ/F11 9.9626 Tf 4.853 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 8.045 0 Td [(+)-222(6)]TJ/F11 9.9626 Tf 14.557 0 Td [(~)461(v)]TJ +0 g 0 G +0 g 0 G +ET +1 0 0 1 316.766 149.606 cm +q +0 G +0 g +0.3985 w +q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +0.59776 w +0 G +0 g +[ ] 0.0 d +1 0 0 rg 1 0 0 RG +0.0 0.0 m +0.0 0.0 l +170.08086 0.0 l +226.77448 113.38724 l +56.69362 113.38724 l +h +S +0 g 0 G +Q +q +0.59776 w +0 G +0 g +[ ] 0.0 d +0 0 1 rg 0 0 1 RG +0.0 0.0 m +0.0 0.0 m +113.38724 113.38724 l +S +0 g 0 G +Q +q +0.59776 w +0 G +0 g +[ ] 0.0 d +0 0 1 rg 0 0 1 RG +56.69362 56.69362 m +56.69362 56.69362 m +170.08086 113.38724 l +S +0 g 0 G +Q +q +0.59776 w +0 G +0 g +[ ] 0.0 d +0 0 1 rg 0 0 1 RG +113.38724 85.0404 m +113.38724 85.0404 m +198.42764 56.69362 l +S +0 g 0 G +Q +q +0 G +0 g +q +0 G +0 g +58.18803 113.38724 m +58.18803 114.21257 57.51895 114.88165 56.69362 114.88165 c +55.86827 114.88165 55.1992 114.21257 55.1992 113.38724 c +55.1992 112.56189 55.86827 111.89282 56.69362 111.89282 c +57.51895 111.89282 58.18803 112.56189 58.18803 113.38724 c +h +56.69362 113.38724 m +B +Q +q +1 0 0 1 56.693 113.386 cm +1.0 0.0 0.0 1.0 0.0 0.0 cm +q +0 G +0 g +Q +1 0 0 1 -56.693 -113.386 cm +Q +Q +q +0 G +0 g +q +0 G +0 g +114.88165 113.38724 m +114.88165 114.21257 114.21257 114.88165 113.38724 114.88165 c +112.56189 114.88165 111.89282 114.21257 111.89282 113.38724 c +111.89282 112.56189 112.56189 111.89282 113.38724 111.89282 c +114.21257 111.89282 114.88165 112.56189 114.88165 113.38724 c +h +113.38724 113.38724 m +B +Q +q +1 0 0 1 113.386 113.386 cm +1.0 0.0 0.0 1.0 0.0 0.0 cm +q +0 G +0 g +Q +1 0 0 1 -113.386 -113.386 cm +Q +Q +q +0 G +0 g +q +0 G +0 g +171.57527 113.38724 m +171.57527 114.21257 170.9062 114.88165 170.08086 114.88165 c +169.25551 114.88165 168.58644 114.21257 168.58644 113.38724 c +168.58644 112.56189 169.25551 111.89282 170.08086 111.89282 c +170.9062 111.89282 171.57527 112.56189 171.57527 113.38724 c +h +170.08086 113.38724 m +B +Q +q +1 0 0 1 170.079 113.386 cm +1.0 0.0 0.0 1.0 0.0 0.0 cm +q +0 G +0 g +Q +1 0 0 1 -170.079 -113.386 cm +Q +Q +q +0 G +0 g +q +0 G +0 g +228.26889 113.38724 m +228.26889 114.21257 227.59982 114.88165 226.77448 114.88165 c +225.94913 114.88165 225.28006 114.21257 225.28006 113.38724 c +225.28006 112.56189 225.94913 111.89282 226.77448 111.89282 c +227.59982 111.89282 228.26889 112.56189 228.26889 113.38724 c +h +226.77448 113.38724 m +B +Q +q +1 0 0 1 226.772 113.386 cm +1.0 0.0 0.0 1.0 0.0 0.0 cm +q +0 G +0 g +Q +1 0 0 1 -226.772 -113.386 cm +Q +Q +q +0 G +0 g +q +0 G +0 g +58.18803 56.69362 m +58.18803 57.51895 57.51895 58.18803 56.69362 58.18803 c +55.86827 58.18803 55.1992 57.51895 55.1992 56.69362 c +55.1992 55.86827 55.86827 55.1992 56.69362 55.1992 c +57.51895 55.1992 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Jones +%Copyright: Copyright (c) 1997, 2009 American Mathematical Society +%Copyright: (), with Reserved Font Name CMR12. +% This Font Software is licensed under the SIL Open Font License, Version 1.1. +% This license is in the accompanying file OFL.txt, and is also +% available with a FAQ at: http://scripts.sil.org/OFL. +%%EndComments +FontDirectory/CMR12 known{/CMR12 findfont dup/UniqueID known{dup +/UniqueID get 5000794 eq exch/FontType get 1 eq and}{pop false}ifelse +{save true}{false}ifelse}{false}ifelse +11 dict begin +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def +/FontName /RLYLLI+CMR12 def +/FontBBox {-34 -251 988 750 }readonly def +/PaintType 0 def +/FontInfo 9 dict dup begin +/version (003.002) readonly def +/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR12.) readonly def +/FullName (CMR12) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 66 /B put +dup 68 /D put +dup 71 /G put +dup 76 /L put +dup 77 /M put +dup 83 /S put +dup 86 /V put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 20 /caron put +dup 44 /comma put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 46 /period put +dup 114 /r put +dup 116 /t put +dup 50 /two put +dup 117 /u put +dup 122 /z put +dup 48 /zero put +readonly def +currentdict end +currentfile eexec +oc;jAw-=%W)-{ru)rAE(@{빴Q|_R +ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ +}3{Z2zݬT2s$Z&{BJ{r̗m1l(zNRr^&%:(/IߺHm!4JxI7bs,OiOl75R 9z(X*Rhn5&g\c9`EgwT!xIJz҈v*lcoƿsdm^%=谺D +u9#3P _] )w +UA8 HuG:DJ(W;]-0<.gSB NlZOLӡ5^9:K*|F +{É ڇE,q>j0^x떲Q'X酉i ;yZPt>p1SV}:ުad0h{JA)Θ[ U=y5pRU&0'-8tIAx*̣$!gRHS;RVU?!lM٬2gO.T7wϓ)?CߠVb7^kJ;c +N* ٍG|Ucͮߢɨl6h6[ 2ߵПZvUlP|%)VǸm׫=&a +Js_̲y|{R6ĴʗB7jIȘ2a% @74 @4(.= `h'p+xvX}?G3D:^ӟ*&4prx5e^hk@S_̎Cl^^}ڶ-q9@e @|wMrc9P(TkruY@MnuW`%?Q8wG3g; dlo 2 Uu6C֋%YT'Rjo1Mn}L+:O/`@ӟӎ4J +B $YaհH Ag0IQ<;v|<6G@tqX>ɏpI%(Xv7}19lAKڮ6]+l_6'3`k*T (]65R-[(EAJ!3s:e*Aܣ ZEsNьmcЪ..> ˆ>Q&x̹znkCfqW-ٕ6qo*p+.gjlZrht?3:2ty&F!w^9vӐy*'ImtӮ:dN#LaRx!d!R *9SDdkb$Vdž^t4}h5eHNrHI,O6'l +NO#xa OTV-(!JZyX !]z@. 5-DL5_rHqg/r秂gͯP%x d꿖xAcŘʺϡYd(*:od`AMPb-nt]#lg&eb5d*OE 5 UThlv9_)$pC+(M ռPVOptcC`ՠ0IJ85YA('针1J ) =n?Epaq\')_4}KY+d>^cV60EZt,)ie Oӟ5ni8B5*Ƅxn@EDP>e$I^na Y>k#w?p͓t!_1 dr{d ,@]+ضCzn{0RUK,&Ձ\ƭТ1LB#Jp0 XJK7ZLD"afI1?jt'8:/(IGʵ6 <+r xj=9zI!ƶreGNXNpA4Us]b;g-L:/ڮpaؖ:1xǔ`V&EE?c CۗǙ77-`$Mv|&sČ 6X!g#ndχ[w䄁n(dَoo_o2<ݻ  xMI^ +[$dDTZ jķi|O.E9wbSsBz֚ȴ!2g6bcrۑW1A"nX14nKOC-NA=9g5=W^x(xڞEt8}NIDʄ!"]}FET2mRi< r3a0!fS&W{V_ ħ/Wc + 15y8/ V㯧٧򁂝*^F}#? 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-13.396 Td [(~)437(a)]TJ/F8 9.9626 Tf 9.21 0 Td [(in)]TJ/F11 9.9626 Tf 10.504 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 7.597 0 Td [(izrazi)]TJ/F14 9.9626 Tf 26.595 6.808 Td [(\000)242(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AC)]TJ/F8 9.9626 Tf 15.305 0 Td [(,)]TJ/F14 9.9626 Tf 6.088 6.808 Td [(\000)363(\000)363(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AM)]TJ/F8 9.9626 Tf 18.223 0 Td [(,)]TJ/F14 9.9626 Tf 6.089 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(M)]TJ/F8 9.9626 Tf 22.129 0 Td [(in)]TJ/F14 9.9626 Tf 11.623 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(B)]TJ/F8 9.9626 Tf 18.808 0 Td [(.)]TJ/F14 9.9626 Tf -48.295 -19.248 Td [(\000)242(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AC)]TJ/F8 9.9626 Tf 18.072 0 Td [(=)]TJ/F11 9.9626 Tf 9.892 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.808 Td [(\000)363(\000)363(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AM)]TJ/F8 9.9626 Tf 20.991 0 Td [(=)]TJ 11.711 6.74 Td [(1)]TJ +ET +q +1 0 0 1 265.673 281.124 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 265.673 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(M)]TJ/F8 9.9626 Tf 21.575 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(\000)]TJ/F8 9.9626 Tf 8.945 6.74 Td [(1)]TJ +ET +q +1 0 0 1 342.353 281.124 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 342.353 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.843 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(;)]TJ/F14 9.9626 Tf 7.748 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(B)]TJ/F8 9.9626 Tf 21.576 0 Td [(=)]TJ 11.711 6.74 Td [(1)]TJ +ET +q +1 0 0 1 411.283 281.124 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 411.283 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F14 9.9626 Tf 8.104 0 Td [(\000)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ +0 g 0 G +/F77 9.9626 Tf -393.983 -23.91 Td [(360.)]TJ +0 g 0 G +/F8 9.9626 Tf 25.349 0 Td [(Na)-279(strani)1(c)-1(ah)-278(paralelograma)]TJ/F11 9.9626 Tf 122.203 0 Td [(AB)-50(C)-72(D)]TJ/F8 9.9626 Tf 34.661 0 Td [(so)-279(dane)-278(to)28(\024)472(ck)28(e)]TJ/F11 9.9626 Tf 60.407 0 Td [(I)]TJ/F8 9.9626 Tf 5.161 0 Td [(,)]TJ/F11 9.9626 Tf 5.651 0 Td [(J)]TJ/F8 9.9626 Tf -228.083 -11.956 Td [(in)]TJ/F11 9.9626 Tf 11.727 0 Td [(K)]TJ/F8 9.9626 Tf 9.174 0 Td [(,)-346(tak)27(o)-343(da)-344(je)]TJ/F14 9.9626 Tf 53.299 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(D)-28(I)]TJ/F14 9.9626 Tf 13.686 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(I)-78(J)]TJ/F14 9.9626 Tf 11.644 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(J)-96(C)]TJ/F14 9.9626 Tf 14.315 0 Td [(j)]TJ/F8 9.9626 Tf 6.193 0 Td [(in)]TJ/F14 9.9626 Tf 11.726 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(B)-50(K)]TJ/F14 9.9626 Tf 17.23 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(K)-72(C)]TJ/F14 9.9626 Tf 17.007 0 Td [(j)]TJ/F8 9.9626 Tf 2.767 0 Td [(.)]TJ -231.798 -11.955 Td [(T)83(o)28(\024)472(ck)56(a)]TJ/F11 9.9626 Tf 28.442 0 Td [(L)]TJ/F8 9.9626 Tf 9.761 0 Td [(je)-299(razp)-28(olo)28(vi)53(\024)447(s)28(\024)472(ce)-300(dalj)1(ico)]TJ/F11 9.9626 Tf 97.307 0 Td [(AI)]TJ/F8 9.9626 Tf 12.633 0 Td [(,)-306(to)28(\024)472(ck)55(a)]TJ/F11 9.9626 Tf 31.768 0 Td [(M)]TJ/F8 9.9626 Tf 13.732 0 Td [(pa)-299(razp)-28(o-)]TJ -193.643 -11.955 Td [(lo)28(vi)53(\024)447(s)28(\024)472(ce)-334(daljice)]TJ/F11 9.9626 Tf 62.876 0 Td [(LJ)]TJ/F8 9.9626 Tf 13.263 0 Td [(.)]TJ +0 g 0 G +/F77 9.9626 Tf -69.227 -19.422 Td [(a\051)]TJ +0 g 0 G +/F8 9.9626 Tf 15.006 0 Td [(Dana)-454(sta)-453(v)28(ektorja)]TJ/F14 9.9626 Tf 84.901 6.808 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AB)]TJ/F8 9.9626 Tf 20.292 0 Td [(=)]TJ/F11 9.9626 Tf 11.889 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 10.409 0 Td [(in)]TJ/F14 9.9626 Tf 12.821 6.808 Td [(\000)480(\000)481(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(C)]TJ/F8 9.9626 Tf 20.654 0 Td [(=)]TJ/F11 9.9626 Tf 11.394 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(.)-805(Izrazi)]TJ -177.754 -13.949 Td [(v)28(ektor)]TJ/F14 9.9626 Tf 30.746 6.807 Td [(\000)278(\000)278(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(M)-109(K)]TJ/F8 9.9626 Tf 23.246 0 Td [(z)-333(v)27(ektorjema)]TJ/F11 9.9626 Tf 58.627 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 9.21 0 Td [(in)]TJ/F11 9.9626 Tf 10.504 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(.)]TJ/F14 9.9626 Tf -67.624 -14.387 Td [(\000)278(\000)278(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(K)]TJ/F8 9.9626 Tf 22.693 0 Td [(=)]TJ 11.712 6.74 Td [(7)]TJ +ET +q +1 0 0 1 196.971 166.782 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 196.971 157.457 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F14 9.9626 Tf 8.104 0 Td [(\000)]TJ/F8 9.9626 Tf 11.158 6.74 Td [(1)]TJ +ET +q +1 0 0 1 221.786 166.782 cm +[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S +Q +BT +/F8 9.9626 Tf 221.786 157.457 Td [(4)]TJ/F11 9.9626 Tf 5.057 9.463 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(;)]TJ +0 g 0 G +/F77 9.9626 Tf -155.578 -24.414 Td [(b\051)]TJ +0 g 0 G +/F8 9.9626 Tf 15.802 0 Td [(Na)-56(j)-445(b)-28(osta)-446(bazna)-445(v)27(ektorja)]TJ/F14 9.9626 Tf 118.303 6.808 Td [(\000)579(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(LI)]TJ/F8 9.9626 Tf 16.575 0 Td [(=)]TJ/F11 9.9626 Tf 12.253 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 10.273 0 Td [(in)]TJ/F14 9.9626 Tf 12.742 6.808 Td [(\000)398(\000)398(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(LM)]TJ/F8 9.9626 Tf 22.165 0 Td [(=)]TJ/F11 9.9626 Tf 11.996 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.573 0 Td [(.)]TJ -209.88 -13.949 Td [(Izrazi)-333(v)27(ektorja)]TJ/F14 9.9626 Tf 66.197 6.807 Td [(\000)475(\000)475(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AD)]TJ/F8 9.9626 Tf 19.317 0 Td [(in)]TJ/F14 9.9626 Tf 11.623 6.807 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AB)]TJ/F8 9.9626 Tf 18.85 0 Td [(z)-333(v)27(ektorjema)]TJ/F11 9.9626 Tf 59.122 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 9.152 0 Td [(in)]TJ/F11 9.9626 Tf 11.236 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.574 0 Td [(.)]TJ/F14 9.9626 Tf -164.571 -11.69 Td [(\000)475(\000)475(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AD)]TJ/F8 9.9626 Tf 18.764 0 Td [(=)-278(3)]TJ/F11 9.9626 Tf 15.369 0 Td [(~)487(u)]TJ/F14 9.9626 Tf 8.046 0 Td [(\000)]TJ/F8 9.9626 Tf 9.963 0 Td [(2)]TJ/F11 9.9626 Tf 4.594 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.573 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.807 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AB)]TJ/F8 9.9626 Tf 18.296 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(3)]TJ/F11 9.9626 Tf 4.853 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 8.045 0 Td [(+)-222(6)]TJ/F11 9.9626 Tf 14.557 0 Td [(~)461(v)]TJ +0 g 0 G +0 g 0 G +ET +1 0 0 1 316.766 149.606 cm +q +0 G +0 g +0.3985 w +q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +Q +q +0.59776 w +0 G +0 g +[ ] 0.0 d +1 0 0 rg 1 0 0 RG +0.0 0.0 m +0.0 0.0 l +170.08086 0.0 l +226.77448 113.38724 l +56.69362 113.38724 l +h +S +0 g 0 G +Q +q +0.59776 w +0 G +0 g +[ ] 0.0 d +0 0 1 rg 0 0 1 RG +0.0 0.0 m +0.0 0.0 m +113.38724 113.38724 l +S +0 g 0 G +Q +q +0.59776 w +0 G +0 g +[ ] 0.0 d +0 0 1 rg 0 0 1 RG +56.69362 56.69362 m +56.69362 56.69362 m +170.08086 113.38724 l +S +0 g 0 G +Q +q +0.59776 w +0 G +0 g +[ ] 0.0 d +0 0 1 rg 0 0 1 RG +113.38724 85.0404 m +113.38724 85.0404 m +198.42764 56.69362 l +S +0 g 0 G +Q +q +0 G +0 g +q +0 G +0 g +58.18803 113.38724 m +58.18803 114.21257 57.51895 114.88165 56.69362 114.88165 c 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+170.9062 111.89282 171.57527 112.56189 171.57527 113.38724 c +h +170.08086 113.38724 m +B +Q +q +1 0 0 1 170.079 113.386 cm +1.0 0.0 0.0 1.0 0.0 0.0 cm +q +0 G +0 g +Q +1 0 0 1 -170.079 -113.386 cm +Q +Q +q +0 G +0 g +q +0 G +0 g +228.26889 113.38724 m +228.26889 114.21257 227.59982 114.88165 226.77448 114.88165 c +225.94913 114.88165 225.28006 114.21257 225.28006 113.38724 c +225.28006 112.56189 225.94913 111.89282 226.77448 111.89282 c +227.59982 111.89282 228.26889 112.56189 228.26889 113.38724 c +h +226.77448 113.38724 m +B +Q +q +1 0 0 1 226.772 113.386 cm +1.0 0.0 0.0 1.0 0.0 0.0 cm +q +0 G +0 g +Q +1 0 0 1 -226.772 -113.386 cm +Q +Q +q +0 G +0 g +q +0 G +0 g +58.18803 56.69362 m +58.18803 57.51895 57.51895 58.18803 56.69362 58.18803 c +55.86827 58.18803 55.1992 57.51895 55.1992 56.69362 c +55.1992 55.86827 55.86827 55.1992 56.69362 55.1992 c +57.51895 55.1992 58.18803 55.86827 58.18803 56.69362 c +h +56.69362 56.69362 m +B +Q +q +1 0 0 1 56.693 56.693 cm +1.0 0.0 0.0 1.0 0.0 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Jones +%Copyright: Copyright (c) 1997, 2009 American Mathematical Society +%Copyright: (), with Reserved Font Name CMR12. +% This Font Software is licensed under the SIL Open Font License, Version 1.1. +% This license is in the accompanying file OFL.txt, and is also +% available with a FAQ at: http://scripts.sil.org/OFL. +%%EndComments +FontDirectory/CMR12 known{/CMR12 findfont dup/UniqueID known{dup +/UniqueID get 5000794 eq exch/FontType get 1 eq and}{pop false}ifelse +{save true}{false}ifelse}{false}ifelse +11 dict begin +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def +/FontName /RLYLLI+CMR12 def +/FontBBox {-34 -251 988 750 }readonly def +/PaintType 0 def +/FontInfo 9 dict dup begin +/version (003.002) readonly def +/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR12.) readonly def +/FullName (CMR12) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 66 /B put +dup 68 /D put +dup 71 /G put +dup 76 /L put +dup 77 /M put +dup 83 /S put +dup 86 /V put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 20 /caron put +dup 44 /comma put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 46 /period put +dup 114 /r put +dup 116 /t put +dup 50 /two put +dup 117 /u put +dup 122 /z put +dup 48 /zero put +readonly def +currentdict end +currentfile eexec +oc;jAw-=%W)-{ru)rAE(@{빴Q|_R +ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ +}3{Z2zݬT2s$Z&{BJ{r̗m1l(zNRr^&%:(/IߺHm!4JxI7bs,OiOl75R 9z(X*Rhn5&g\c9`EgwT!xIJz҈v*lcoƿsdm^%=谺D +u9#3P _] )w +UA8 HuG:DJ(W;]-0<.gSB NlZOLӡ5^9:K*|F +{É ڇE,q>j0^x떲Q'X酉i ;yZPt>p1SV}:ުad0h{JA)Θ[ U=y5pRU&0'-8tIAx*̣$!gRHS;RVU?!lM٬2gO.T7wϓ)?CߠVb7^kJ;c +N* ٍG|Ucͮߢɨl6h6[ 2ߵПZvUlP|%)VǸm׫=&a +Js_̲y|{R6ĴʗB7jIȘ2a% @74 @4(.= `h'p+xvX}?G3D:^ӟ*&4prx5e^hk@S_̎Cl^^}ڶ-q9@e @|wMrc9P(TkruY@MnuW`%?Q8wG3g; dlo 2 Uu6C֋%YT'Rjo1Mn}L+:O/`@ӟӎ4J +B $YaհH Ag0IQ<;v|<6G@tqX>ɏpI%(Xv7}19lAKڮ6]+l_6'3`k*T (]65R-[(EAJ!3s:e*Aܣ ZEsNьmcЪ..> ˆ>Q&x̹znkCfqW-ٕ6qo*p+.gjlZrht?3:2ty&F!w^9vӐy*'ImtӮ:dN#LaRx!d!R *9SDdkb$Vdž^t4}h5eHNrHI,O6'l +NO#xa OTV-(!JZyX !]z@. 5-DL5_rHqg/r秂gͯP%x d꿖xAcŘʺϡYd(*:od`AMPb-nt]#lg&eb5d*OE 5 UThlv9_)$pC+(M ռPVOptcC`ՠ0IJ85YA('针1J ) =n?Epaq\')_4}KY+d>^cV60EZt,)ie Oӟ5ni8B5*Ƅxn@EDP>e$I^na Y>k#w?p͓t!_1 dr{d ,@]+ضCzn{0RUK,&Ձ\ƭТ1LB#Jp0 XJK7ZLD"afI1?jt'8:/(IGʵ6 <+r xj=9zI!ƶreGNXNpA4Us]b;g-L:/ڮpaؖ:1xǔ`V&EE?c CۗǙ77-`$Mv|&sČ 6X!g#ndχ[w䄁n(dَoo_o2<ݻ  xMI^ +[$dDTZ jķi|O.E9wbSsBz֚ȴ!2g6bcrۑW1A"nX14nKOC-NA=9g5=W^x(xڞEt8}NIDʄ!"]}FET2mRi< r3a0!fS&W{V_ ħ/Wc + 15y8/ V㯧٧򁂝*^F}#? 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Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbral naključno. +Ta dokument vsebuje domačo nalogo, ki zajema snov \textit{\snovdn}pri matematiki. Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbral naključno. \end{abstract} \tableofcontents \section{Vaje \textit{Matematika 2}: stran 55, štiri naloge 349-361} @@ -140,11 +140,25 @@ Ta dokument vsebuje domačo nalogo, ki zajema snov \textit{\snovdn}pri matematik $\Vec{m}=-2\Vec{a}+\frac{3}{2}\Vec{b}+\Vec{c}$ in $\Vec{n}=-\frac{1}{2}\Vec{a}+\Vec{b}+2\Vec{c}$. Vektor $2\Vec{m}-\Vec{n}$ zapiši v dani bazi. % 350 - \setcoutner{enumi}{351} + $$ + 2\Vec{m}-\Vec{n}=-\frac{7}{2}\Vec{a}+\frac{1}{3}\Vec{b} + $$ + \setcounter{enumi}{351} \item Točke $A$, $B$, $C$, $D$ in $E$ ležijo na premici tako, da je $|AB|:|BC|:|CD|:|DE|=3:2:1:3$. Točki $B$ in $D$ ležita med $A$ in $C$. točka $D$ pa med $B$ in $E$. Naj bo vektor $\Vec{a}=\vektor{BE}$ bazni vektor. Z vektorjem $\Vec{a}$ izrazi vektorje $\vektor{DC}$, $\vektor{AC}$ in $\vektor{DE}$. % 352 + $$ + \vektor{DC} = \frac{1}{4}\Vec{a};\ % + \vektor{AC} = \frac{5}{3}\Vec{a};\ % + \vektor{DE} = \frac{3}{4}\Vec{a}% + $$ \item Točka $M$ je razpolovišče daljice $CD$ pravokotnika $ABCD$, vektorja $\Vec{a}=\vektor{AB}$ in $\Vec{b}=\vektor{AD}$ sta bazna vektorja. Z $\Vec{a}$ in $\Vec{b}$ izrazi $\vektor{AC}$, $\vektor{AM}$, $\vektor{BM}$ in $\vektor{MB}$. % 353 + $$ + \vektor{AC} = \Vec{a}+\Vec{b};\ % + \vektor{AM} = \frac{1}{2}\Vec{a}+\Vec{b};\ % + \vektor{BM} = -\frac{1}{2}\Vec{a}+\Vec{b};\ % + \vektor{MB} = \frac{1}{2}\Vec{a}-\Vec{b};\ % + $$ \setcounter{enumi}{359} \item % 360 \begin{multicols}{2} @@ -153,9 +167,16 @@ Ta dokument vsebuje domačo nalogo, ki zajema snov \textit{\snovdn}pri matematik \begin{enumerate}[label=\textbf{\xslalph*)}] \item Dana sta vektorja $\vektor{AB}=\Vec{a}$ in $\vektor{BC}=\Vec{b}$. Izrazi vektor $\vektor{MK}$ z vektorjema $\Vec{a}$ in $\Vec{b}$. + $$ + \vektor{MK} = \frac{7}{2}\Vec{a}-\frac{1}{4}\Vec{b}; + $$ \item Naj bosta bazna vektorja $\vektor{LI}=\Vec{u}$ in $\vektor{LM}=\Vec{v}$. Izrazi vektorja $\vektor{AD}$ in $\vektor{AB}$ z vektorjema $\Vec{u}$ in $\Vec{v}$. + $$ + \vektor{AD} = 3\Vec{u}-2\Vec{v};\ % + \vektor{AB} = -3\Vec{u}+6\Vec{v} + $$ \end{enumerate} \vfill\null\columnbreak \begin{tikzpicture}[scale=2] diff --git a/mat/domace_naloge/21/dokument.toc b/mat/domace_naloge/21/dokument.toc index 3358445..6606006 100644 --- a/mat/domace_naloge/21/dokument.toc +++ b/mat/domace_naloge/21/dokument.toc @@ -1,4 +1,4 @@ \babel@toc {slovene}{} \babel@toc {slovene}{} \contentsline {section}{\numberline {1}Vaje \textit {Matematika 2}: stran 55, štiri naloge 349-361}{1}{section.1}% -\contentsline {section}{\numberline {2}Zaključek}{1}{section.2}% +\contentsline {section}{\numberline {2}Zaključek}{2}{section.2}% diff --git a/mat/domace_naloge/21/stderr.log b/mat/domace_naloge/21/stderr.log index 7464410..2017c6d 100644 --- a/mat/domace_naloge/21/stderr.log +++ b/mat/domace_naloge/21/stderr.log @@ -1 +1 @@ -<<75F40139103067DB4935B23B6287835A>]/Index[ 0 143]/Info 141 0 R/Length 369/Root 140 0 R/Size 143/W[ 1 3 1]>> +<<8BDE9569A286CF89B3E0C7EE8CAF8343>]/Index[ 0 143]/Info 141 0 R/Length 372/Root 140 0 R/Size 143/W[ 1 3 1]>> diff --git a/mat/domace_naloge/21/stdout.log b/mat/domace_naloge/21/stdout.log index df1ebbc..b547d19 100644 --- a/mat/domace_naloge/21/stdout.log +++ b/mat/domace_naloge/21/stdout.log @@ -205,311 +205,8 @@ zlibrarydecorations.code.tex (/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduledecorations.cod e.tex)) (/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibrarydecorations.pathmorphing.code.tex -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/decorations/pgflibrary -decorations.pathmorphing.code.tex)) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibrarydecorations.pathreplacing.code.tex -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/decorations/pgflibrary -decorations.pathreplacing.code.tex))) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibraryplotmarks.code.tex -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryplotmarks.co -de.tex))) (/usr/share/texlive/texmf-dist/tex/latex/enumitem/enumitem.sty) -(/usr/share/texlive/texmf-dist/tex/latex/siunitx/siunitx.sty -(/usr/share/texlive/texmf-dist/tex/latex/l3kernel/expl3.sty -(/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def)) -(/usr/share/texlive/texmf-dist/tex/latex/l3packages/xparse/xparse.sty) -(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty -(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty)) -(/usr/share/texlive/texmf-dist/tex/latex/tools/array.sty) -(/usr/share/texlive/texmf-dist/tex/latex/l3packages/l3keys2e/l3keys2e.sty) -(/usr/share/texlive/texmf-dist/tex/latex/translator/translator.sty)) -(/usr/share/texlive/texmf-dist/tex/latex/tools/multicol.sty) -(/usr/share/texlive/texmf-dist/tex/latex/tabularcalc/tabularcalc.sty -(/usr/share/texlive/texmf-dist/tex/latex/fp/fp.sty -`Fixed Point Package', Version 0.8, April 2, 1995 (C) Michael Mehlich -(/usr/share/texlive/texmf-dist/tex/latex/fp/defpattern.sty) -(/usr/share/texlive/texmf-dist/tex/latex/fp/fp-basic.sty) -(/usr/share/texlive/texmf-dist/tex/latex/fp/fp-addons.sty) -(/usr/share/texlive/texmf-dist/tex/latex/fp/fp-snap.sty) -(/usr/share/texlive/texmf-dist/tex/latex/fp/fp-exp.sty) -(/usr/share/texlive/texmf-dist/tex/latex/fp/fp-trigo.sty) -(/usr/share/texlive/texmf-dist/tex/latex/fp/fp-pas.sty) -(/usr/share/texlive/texmf-dist/tex/latex/fp/fp-random.sty) -(/usr/share/texlive/texmf-dist/tex/latex/fp/fp-eqn.sty) -(/usr/share/texlive/texmf-dist/tex/latex/fp/fp-upn.sty) -(/usr/share/texlive/texmf-dist/tex/latex/fp/fp-eval.sty)) -(/usr/share/texlive/texmf-dist/tex/generic/xstring/xstring.sty -(/usr/share/texlive/texmf-dist/tex/generic/xstring/xstring.tex)) -(/usr/share/texlive/texmf-dist/tex/latex/numprint/numprint.sty -No configuration file `numprint.cfg' found.)) -(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty -For additional information on amsmath, use the `?' option. -(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty) -(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)) -(/usr/share/texlive/texmf-dist/tex/latex/float/float.sty) -(/usr/share/texlive/texmf-dist/tex/latex/tasks/tasks.sty -(/usr/share/texlive/texmf-dist/tex/latex/l3packages/xtemplate/xtemplate.sty) -(/usr/share/texlive/texmf-dist/tex/latex/tasks/tasks.cfg)) -(/usr/share/texlive/texmf-dist/tex/latex/filecontents/filecontents.sty - -Package filecontents Warning: This package is obsolete. 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-6.808 Td [(AD)]TJ/F8 9.9626 Tf 19.454 0 Td [(sta)-347(bazna)-347(v)28(ektorja.)-486(Z)]TJ/F11 9.9626 Tf -385.411 -13.396 Td [(~)437(a)]TJ/F8 9.9626 Tf 9.21 0 Td [(in)]TJ/F11 9.9626 Tf 10.504 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 7.597 0 Td [(izrazi)]TJ/F14 9.9626 Tf 26.595 6.808 Td [(\000)242(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AC)]TJ/F8 9.9626 Tf 15.305 0 Td [(,)]TJ/F14 9.9626 Tf 6.088 6.808 Td [(\000)363(\000)363(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AM)]TJ/F8 9.9626 Tf 18.223 0 Td [(,)]TJ/F14 9.9626 Tf 6.089 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(M)]TJ/F8 9.9626 Tf 22.129 0 Td [(in)]TJ/F14 9.9626 Tf 11.623 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(B)]TJ/F8 9.9626 Tf 18.808 0 Td [(.)]TJ/F14 9.9626 Tf -48.295 -19.248 Td [(\000)242(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AC)]TJ/F8 9.9626 Tf 18.072 0 Td [(=)]TJ/F11 9.9626 Tf 9.892 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.808 Td [(\000)363(\000)363(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AM)]TJ/F8 9.9626 Tf 20.991 0 Td [(=)]TJ 11.711 6.74 Td [(1)]TJ -ET -q -1 0 0 1 265.673 281.124 cm -[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S -Q -BT -/F8 9.9626 Tf 265.673 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(M)]TJ/F8 9.9626 Tf 21.575 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(\000)]TJ/F8 9.9626 Tf 8.945 6.74 Td [(1)]TJ -ET -q -1 0 0 1 342.353 281.124 cm -[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S -Q -BT -/F8 9.9626 Tf 342.353 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.843 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(;)]TJ/F14 9.9626 Tf 7.748 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(B)]TJ/F8 9.9626 Tf 21.576 0 Td [(=)]TJ 11.711 6.74 Td [(1)]TJ -ET -q -1 0 0 1 411.283 281.124 cm -[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S -Q -BT -/F8 9.9626 Tf 411.283 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F14 9.9626 Tf 8.104 0 Td [(\000)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ -0 g 0 G -/F77 9.9626 Tf -393.983 -23.91 Td [(360.)]TJ -0 g 0 G -/F8 9.9626 Tf 25.349 0 Td [(Na)-279(strani)1(c)-1(ah)-278(paralelograma)]TJ/F11 9.9626 Tf 122.203 0 Td [(AB)-50(C)-72(D)]TJ/F8 9.9626 Tf 34.661 0 Td [(so)-279(dane)-278(to)28(\024)472(ck)28(e)]TJ/F11 9.9626 Tf 60.407 0 Td [(I)]TJ/F8 9.9626 Tf 5.161 0 Td [(,)]TJ/F11 9.9626 Tf 5.651 0 Td [(J)]TJ/F8 9.9626 Tf -228.083 -11.956 Td [(in)]TJ/F11 9.9626 Tf 11.727 0 Td [(K)]TJ/F8 9.9626 Tf 9.174 0 Td [(,)-346(tak)27(o)-343(da)-344(je)]TJ/F14 9.9626 Tf 53.299 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(D)-28(I)]TJ/F14 9.9626 Tf 13.686 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(I)-78(J)]TJ/F14 9.9626 Tf 11.644 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(J)-96(C)]TJ/F14 9.9626 Tf 14.315 0 Td [(j)]TJ/F8 9.9626 Tf 6.193 0 Td [(in)]TJ/F14 9.9626 Tf 11.726 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(B)-50(K)]TJ/F14 9.9626 Tf 17.23 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(K)-72(C)]TJ/F14 9.9626 Tf 17.007 0 Td [(j)]TJ/F8 9.9626 Tf 2.767 0 Td [(.)]TJ -231.798 -11.955 Td [(T)83(o)28(\024)472(ck)56(a)]TJ/F11 9.9626 Tf 28.442 0 Td [(L)]TJ/F8 9.9626 Tf 9.761 0 Td [(je)-299(razp)-28(olo)28(vi)53(\024)447(s)28(\024)472(ce)-300(dalj)1(ico)]TJ/F11 9.9626 Tf 97.307 0 Td [(AI)]TJ/F8 9.9626 Tf 12.633 0 Td [(,)-306(to)28(\024)472(ck)55(a)]TJ/F11 9.9626 Tf 31.768 0 Td [(M)]TJ/F8 9.9626 Tf 13.732 0 Td [(pa)-299(razp)-28(o-)]TJ -193.643 -11.955 Td [(lo)28(vi)53(\024)447(s)28(\024)472(ce)-334(daljice)]TJ/F11 9.9626 Tf 62.876 0 Td [(LJ)]TJ/F8 9.9626 Tf 13.263 0 Td [(.)]TJ -0 g 0 G -/F77 9.9626 Tf -69.227 -19.422 Td [(a\051)]TJ -0 g 0 G -/F8 9.9626 Tf 15.006 0 Td [(Dana)-454(sta)-453(v)28(ektorja)]TJ/F14 9.9626 Tf 84.901 6.808 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AB)]TJ/F8 9.9626 Tf 20.292 0 Td [(=)]TJ/F11 9.9626 Tf 11.889 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 10.409 0 Td [(in)]TJ/F14 9.9626 Tf 12.821 6.808 Td [(\000)480(\000)481(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(C)]TJ/F8 9.9626 Tf 20.654 0 Td [(=)]TJ/F11 9.9626 Tf 11.394 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(.)-805(Izrazi)]TJ -177.754 -13.949 Td [(v)28(ektor)]TJ/F14 9.9626 Tf 30.746 6.807 Td [(\000)278(\000)278(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(M)-109(K)]TJ/F8 9.9626 Tf 23.246 0 Td [(z)-333(v)27(ektorjema)]TJ/F11 9.9626 Tf 58.627 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 9.21 0 Td [(in)]TJ/F11 9.9626 Tf 10.504 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(.)]TJ/F14 9.9626 Tf -67.624 -14.387 Td [(\000)278(\000)278(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(K)]TJ/F8 9.9626 Tf 22.693 0 Td [(=)]TJ 11.712 6.74 Td [(7)]TJ -ET -q -1 0 0 1 196.971 166.782 cm -[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S -Q -BT -/F8 9.9626 Tf 196.971 157.457 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F14 9.9626 Tf 8.104 0 Td [(\000)]TJ/F8 9.9626 Tf 11.158 6.74 Td [(1)]TJ -ET -q -1 0 0 1 221.786 166.782 cm -[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S -Q -BT -/F8 9.9626 Tf 221.786 157.457 Td [(4)]TJ/F11 9.9626 Tf 5.057 9.463 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(;)]TJ -0 g 0 G -/F77 9.9626 Tf -155.578 -24.414 Td [(b\051)]TJ -0 g 0 G -/F8 9.9626 Tf 15.802 0 Td [(Na)-56(j)-445(b)-28(osta)-446(bazna)-445(v)27(ektorja)]TJ/F14 9.9626 Tf 118.303 6.808 Td [(\000)579(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(LI)]TJ/F8 9.9626 Tf 16.575 0 Td [(=)]TJ/F11 9.9626 Tf 12.253 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 10.273 0 Td [(in)]TJ/F14 9.9626 Tf 12.742 6.808 Td [(\000)398(\000)398(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(LM)]TJ/F8 9.9626 Tf 22.165 0 Td [(=)]TJ/F11 9.9626 Tf 11.996 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.573 0 Td [(.)]TJ -209.88 -13.949 Td [(Izrazi)-333(v)27(ektorja)]TJ/F14 9.9626 Tf 66.197 6.807 Td [(\000)475(\000)475(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AD)]TJ/F8 9.9626 Tf 19.317 0 Td [(in)]TJ/F14 9.9626 Tf 11.623 6.807 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AB)]TJ/F8 9.9626 Tf 18.85 0 Td [(z)-333(v)27(ektorjema)]TJ/F11 9.9626 Tf 59.122 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 9.152 0 Td [(in)]TJ/F11 9.9626 Tf 11.236 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.574 0 Td [(.)]TJ/F14 9.9626 Tf -164.571 -11.69 Td [(\000)475(\000)475(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AD)]TJ/F8 9.9626 Tf 18.764 0 Td [(=)-278(3)]TJ/F11 9.9626 Tf 15.369 0 Td [(~)487(u)]TJ/F14 9.9626 Tf 8.046 0 Td [(\000)]TJ/F8 9.9626 Tf 9.963 0 Td [(2)]TJ/F11 9.9626 Tf 4.594 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.573 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.807 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AB)]TJ/F8 9.9626 Tf 18.296 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(3)]TJ/F11 9.9626 Tf 4.853 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 8.045 0 Td [(+)-222(6)]TJ/F11 9.9626 Tf 14.557 0 Td [(~)461(v)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 316.766 149.606 cm -q -0 G -0 g -0.3985 w -q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -0.59776 w -0 G -0 g -[ ] 0.0 d -1 0 0 rg 1 0 0 RG -0.0 0.0 m -0.0 0.0 l -170.08086 0.0 l -226.77448 113.38724 l -56.69362 113.38724 l -h -S -0 g 0 G -Q -q -0.59776 w -0 G -0 g -[ ] 0.0 d -0 0 1 rg 0 0 1 RG -0.0 0.0 m -0.0 0.0 m -113.38724 113.38724 l -S -0 g 0 G -Q -q -0.59776 w -0 G -0 g -[ ] 0.0 d -0 0 1 rg 0 0 1 RG -56.69362 56.69362 m -56.69362 56.69362 m -170.08086 113.38724 l -S -0 g 0 G -Q -q -0.59776 w -0 G -0 g -[ ] 0.0 d -0 0 1 rg 0 0 1 RG -113.38724 85.0404 m -113.38724 85.0404 m -198.42764 56.69362 l -S -0 g 0 G 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114.88165 168.58644 114.21257 168.58644 113.38724 c -168.58644 112.56189 169.25551 111.89282 170.08086 111.89282 c -170.9062 111.89282 171.57527 112.56189 171.57527 113.38724 c -h -170.08086 113.38724 m -B -Q -q -1 0 0 1 170.079 113.386 cm -1.0 0.0 0.0 1.0 0.0 0.0 cm -q -0 G -0 g -Q -1 0 0 1 -170.079 -113.386 cm -Q -Q -q -0 G -0 g -q -0 G -0 g -228.26889 113.38724 m -228.26889 114.21257 227.59982 114.88165 226.77448 114.88165 c -225.94913 114.88165 225.28006 114.21257 225.28006 113.38724 c -225.28006 112.56189 225.94913 111.89282 226.77448 111.89282 c -227.59982 111.89282 228.26889 112.56189 228.26889 113.38724 c -h -226.77448 113.38724 m -B -Q -q -1 0 0 1 226.772 113.386 cm -1.0 0.0 0.0 1.0 0.0 0.0 cm -q -0 G -0 g -Q -1 0 0 1 -226.772 -113.386 cm -Q -Q -q -0 G -0 g -q -0 G -0 g -58.18803 56.69362 m -58.18803 57.51895 57.51895 58.18803 56.69362 58.18803 c -55.86827 58.18803 55.1992 57.51895 55.1992 56.69362 c -55.1992 55.86827 55.86827 55.1992 56.69362 55.1992 c -57.51895 55.1992 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-13.396 Td [(~)437(a)]TJ/F8 9.9626 Tf 9.21 0 Td [(in)]TJ/F11 9.9626 Tf 10.504 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 7.597 0 Td [(izrazi)]TJ/F14 9.9626 Tf 26.595 6.808 Td [(\000)242(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AC)]TJ/F8 9.9626 Tf 15.305 0 Td [(,)]TJ/F14 9.9626 Tf 6.088 6.808 Td [(\000)363(\000)363(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AM)]TJ/F8 9.9626 Tf 18.223 0 Td [(,)]TJ/F14 9.9626 Tf 6.089 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(M)]TJ/F8 9.9626 Tf 22.129 0 Td [(in)]TJ/F14 9.9626 Tf 11.623 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(B)]TJ/F8 9.9626 Tf 18.808 0 Td [(.)]TJ/F14 9.9626 Tf -48.295 -19.248 Td [(\000)242(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AC)]TJ/F8 9.9626 Tf 18.072 0 Td [(=)]TJ/F11 9.9626 Tf 9.892 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.808 Td [(\000)363(\000)363(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AM)]TJ/F8 9.9626 Tf 20.991 0 Td [(=)]TJ 11.711 6.74 Td [(1)]TJ -ET -q -1 0 0 1 265.673 281.124 cm -[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S -Q -BT -/F8 9.9626 Tf 265.673 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(M)]TJ/F8 9.9626 Tf 21.575 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(\000)]TJ/F8 9.9626 Tf 8.945 6.74 Td [(1)]TJ -ET -q -1 0 0 1 342.353 281.124 cm -[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S -Q -BT -/F8 9.9626 Tf 342.353 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F8 9.9626 Tf 8.104 0 Td [(+)]TJ/F11 9.9626 Tf 8.843 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(;)]TJ/F14 9.9626 Tf 7.748 6.808 Td [(\000)334(\000)334(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(B)]TJ/F8 9.9626 Tf 21.576 0 Td [(=)]TJ 11.711 6.74 Td [(1)]TJ -ET -q -1 0 0 1 411.283 281.124 cm -[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S -Q -BT -/F8 9.9626 Tf 411.283 271.799 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F14 9.9626 Tf 8.104 0 Td [(\000)]TJ/F11 9.9626 Tf 8.844 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(;)]TJ -0 g 0 G -/F77 9.9626 Tf -393.983 -23.91 Td [(360.)]TJ -0 g 0 G -/F8 9.9626 Tf 25.349 0 Td [(Na)-279(strani)1(c)-1(ah)-278(paralelograma)]TJ/F11 9.9626 Tf 122.203 0 Td [(AB)-50(C)-72(D)]TJ/F8 9.9626 Tf 34.661 0 Td [(so)-279(dane)-278(to)28(\024)472(ck)28(e)]TJ/F11 9.9626 Tf 60.407 0 Td [(I)]TJ/F8 9.9626 Tf 5.161 0 Td [(,)]TJ/F11 9.9626 Tf 5.651 0 Td [(J)]TJ/F8 9.9626 Tf -228.083 -11.956 Td [(in)]TJ/F11 9.9626 Tf 11.727 0 Td [(K)]TJ/F8 9.9626 Tf 9.174 0 Td [(,)-346(tak)27(o)-343(da)-344(je)]TJ/F14 9.9626 Tf 53.299 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(D)-28(I)]TJ/F14 9.9626 Tf 13.686 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(I)-78(J)]TJ/F14 9.9626 Tf 11.644 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(J)-96(C)]TJ/F14 9.9626 Tf 14.315 0 Td [(j)]TJ/F8 9.9626 Tf 6.193 0 Td [(in)]TJ/F14 9.9626 Tf 11.726 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(B)-50(K)]TJ/F14 9.9626 Tf 17.23 0 Td [(j)]TJ/F8 9.9626 Tf 5.708 0 Td [(=)]TJ/F14 9.9626 Tf 10.689 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(K)-72(C)]TJ/F14 9.9626 Tf 17.007 0 Td [(j)]TJ/F8 9.9626 Tf 2.767 0 Td [(.)]TJ -231.798 -11.955 Td [(T)83(o)28(\024)472(ck)56(a)]TJ/F11 9.9626 Tf 28.442 0 Td [(L)]TJ/F8 9.9626 Tf 9.761 0 Td [(je)-299(razp)-28(olo)28(vi)53(\024)447(s)28(\024)472(ce)-300(dalj)1(ico)]TJ/F11 9.9626 Tf 97.307 0 Td [(AI)]TJ/F8 9.9626 Tf 12.633 0 Td [(,)-306(to)28(\024)472(ck)55(a)]TJ/F11 9.9626 Tf 31.768 0 Td [(M)]TJ/F8 9.9626 Tf 13.732 0 Td [(pa)-299(razp)-28(o-)]TJ -193.643 -11.955 Td [(lo)28(vi)53(\024)447(s)28(\024)472(ce)-334(daljice)]TJ/F11 9.9626 Tf 62.876 0 Td [(LJ)]TJ/F8 9.9626 Tf 13.263 0 Td [(.)]TJ -0 g 0 G -/F77 9.9626 Tf -69.227 -19.422 Td [(a\051)]TJ -0 g 0 G -/F8 9.9626 Tf 15.006 0 Td [(Dana)-454(sta)-453(v)28(ektorja)]TJ/F14 9.9626 Tf 84.901 6.808 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(AB)]TJ/F8 9.9626 Tf 20.292 0 Td [(=)]TJ/F11 9.9626 Tf 11.889 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 10.409 0 Td [(in)]TJ/F14 9.9626 Tf 12.821 6.808 Td [(\000)480(\000)481(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(B)-50(C)]TJ/F8 9.9626 Tf 20.654 0 Td [(=)]TJ/F11 9.9626 Tf 11.394 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.275 0 Td [(.)-805(Izrazi)]TJ -177.754 -13.949 Td [(v)28(ektor)]TJ/F14 9.9626 Tf 30.746 6.807 Td [(\000)278(\000)278(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(M)-109(K)]TJ/F8 9.9626 Tf 23.246 0 Td [(z)-333(v)27(ektorjema)]TJ/F11 9.9626 Tf 58.627 0 Td [(~)437(a)]TJ/F8 9.9626 Tf 9.21 0 Td [(in)]TJ/F11 9.9626 Tf 10.504 2.629 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(.)]TJ/F14 9.9626 Tf -67.624 -14.387 Td [(\000)278(\000)278(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(M)-109(K)]TJ/F8 9.9626 Tf 22.693 0 Td [(=)]TJ 11.712 6.74 Td [(7)]TJ -ET -q -1 0 0 1 196.971 166.782 cm -[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S -Q -BT -/F8 9.9626 Tf 196.971 157.457 Td [(2)]TJ/F11 9.9626 Tf 5.553 6.834 Td [(~)437(a)]TJ/F14 9.9626 Tf 8.104 0 Td [(\000)]TJ/F8 9.9626 Tf 11.158 6.74 Td [(1)]TJ -ET -q -1 0 0 1 221.786 166.782 cm -[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S -Q -BT -/F8 9.9626 Tf 221.786 157.457 Td [(4)]TJ/F11 9.9626 Tf 5.057 9.463 Td [(~)]TJ 1.119 -2.629 Td [(b)]TJ/F8 9.9626 Tf 4.276 0 Td [(;)]TJ -0 g 0 G -/F77 9.9626 Tf -155.578 -24.414 Td [(b\051)]TJ -0 g 0 G -/F8 9.9626 Tf 15.802 0 Td [(Na)-56(j)-445(b)-28(osta)-446(bazna)-445(v)27(ektorja)]TJ/F14 9.9626 Tf 118.303 6.808 Td [(\000)579(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(LI)]TJ/F8 9.9626 Tf 16.575 0 Td [(=)]TJ/F11 9.9626 Tf 12.253 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 10.273 0 Td [(in)]TJ/F14 9.9626 Tf 12.742 6.808 Td [(\000)398(\000)398(!)]TJ/F11 9.9626 Tf 0 -6.808 Td [(LM)]TJ/F8 9.9626 Tf 22.165 0 Td [(=)]TJ/F11 9.9626 Tf 11.996 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.573 0 Td [(.)]TJ -209.88 -13.949 Td [(Izrazi)-333(v)27(ektorja)]TJ/F14 9.9626 Tf 66.197 6.807 Td [(\000)475(\000)475(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AD)]TJ/F8 9.9626 Tf 19.317 0 Td [(in)]TJ/F14 9.9626 Tf 11.623 6.807 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AB)]TJ/F8 9.9626 Tf 18.85 0 Td [(z)-333(v)27(ektorjema)]TJ/F11 9.9626 Tf 59.122 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 9.152 0 Td [(in)]TJ/F11 9.9626 Tf 11.236 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.574 0 Td [(.)]TJ/F14 9.9626 Tf -164.571 -11.69 Td [(\000)475(\000)475(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AD)]TJ/F8 9.9626 Tf 18.764 0 Td [(=)-278(3)]TJ/F11 9.9626 Tf 15.369 0 Td [(~)487(u)]TJ/F14 9.9626 Tf 8.046 0 Td [(\000)]TJ/F8 9.9626 Tf 9.963 0 Td [(2)]TJ/F11 9.9626 Tf 4.594 0 Td [(~)461(v)]TJ/F8 9.9626 Tf 5.573 0 Td [(;)]TJ/F14 9.9626 Tf 7.749 6.807 Td [(\000)498(\000)499(!)]TJ/F11 9.9626 Tf 0 -6.807 Td [(AB)]TJ/F8 9.9626 Tf 18.296 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(3)]TJ/F11 9.9626 Tf 4.853 0 Td [(~)487(u)]TJ/F8 9.9626 Tf 8.045 0 Td [(+)-222(6)]TJ/F11 9.9626 Tf 14.557 0 Td [(~)461(v)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 316.766 149.606 cm -q -0 G -0 g -0.3985 w -q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -Q -q -0.59776 w -0 G -0 g -[ ] 0.0 d -1 0 0 rg 1 0 0 RG -0.0 0.0 m -0.0 0.0 l -170.08086 0.0 l -226.77448 113.38724 l -56.69362 113.38724 l -h -S -0 g 0 G -Q -q -0.59776 w -0 G -0 g -[ ] 0.0 d -0 0 1 rg 0 0 1 RG -0.0 0.0 m -0.0 0.0 m -113.38724 113.38724 l -S -0 g 0 G -Q -q -0.59776 w -0 G -0 g -[ ] 0.0 d -0 0 1 rg 0 0 1 RG -56.69362 56.69362 m -56.69362 56.69362 m -170.08086 113.38724 l -S -0 g 0 G -Q -q -0.59776 w -0 G -0 g -[ ] 0.0 d -0 0 1 rg 0 0 1 RG -113.38724 85.0404 m -113.38724 85.0404 m -198.42764 56.69362 l -S -0 g 0 G -Q -q -0 G -0 g -q -0 G -0 g -58.18803 113.38724 m -58.18803 114.21257 57.51895 114.88165 56.69362 114.88165 c -55.86827 114.88165 55.1992 114.21257 55.1992 113.38724 c -55.1992 112.56189 55.86827 111.89282 56.69362 111.89282 c -57.51895 111.89282 58.18803 112.56189 58.18803 113.38724 c -h -56.69362 113.38724 m -B -Q -q -1 0 0 1 56.693 113.386 cm -1.0 0.0 0.0 1.0 0.0 0.0 cm -q -0 G -0 g -Q -1 0 0 1 -56.693 -113.386 cm -Q -Q -q -0 G -0 g -q -0 G -0 g -114.88165 113.38724 m -114.88165 114.21257 114.21257 114.88165 113.38724 114.88165 c -112.56189 114.88165 111.89282 114.21257 111.89282 113.38724 c -111.89282 112.56189 112.56189 111.89282 113.38724 111.89282 c -114.21257 111.89282 114.88165 112.56189 114.88165 113.38724 c -h -113.38724 113.38724 m -B -Q -q -1 0 0 1 113.386 113.386 cm -1.0 0.0 0.0 1.0 0.0 0.0 cm -q -0 G -0 g -Q -1 0 0 1 -113.386 -113.386 cm -Q -Q -q -0 G -0 g -q -0 G -0 g -171.57527 113.38724 m -171.57527 114.21257 170.9062 114.88165 170.08086 114.88165 c -169.25551 114.88165 168.58644 114.21257 168.58644 113.38724 c -168.58644 112.56189 169.25551 111.89282 170.08086 111.89282 c -170.9062 111.89282 171.57527 112.56189 171.57527 113.38724 c -h -170.08086 113.38724 m -B -Q -q -1 0 0 1 170.079 113.386 cm -1.0 0.0 0.0 1.0 0.0 0.0 cm -q -0 G -0 g -Q -1 0 0 1 -170.079 -113.386 cm -Q -Q -q -0 G -0 g -q -0 G -0 g -228.26889 113.38724 m -228.26889 114.21257 227.59982 114.88165 226.77448 114.88165 c -225.94913 114.88165 225.28006 114.21257 225.28006 113.38724 c -225.28006 112.56189 225.94913 111.89282 226.77448 111.89282 c -227.59982 111.89282 228.26889 112.56189 228.26889 113.38724 c -h -226.77448 113.38724 m -B -Q -q -1 0 0 1 226.772 113.386 cm -1.0 0.0 0.0 1.0 0.0 0.0 cm -q -0 G -0 g -Q -1 0 0 1 -226.772 -113.386 cm -Q -Q -q -0 G -0 g -q -0 G -0 g -58.18803 56.69362 m -58.18803 57.51895 57.51895 58.18803 56.69362 58.18803 c -55.86827 58.18803 55.1992 57.51895 55.1992 56.69362 c -55.1992 55.86827 55.86827 55.1992 56.69362 55.1992 c -57.51895 55.1992 58.18803 55.86827 58.18803 56.69362 c -h -56.69362 56.69362 m -B -Q -q -1 0 0 1 56.693 56.693 cm -1.0 0.0 0.0 1.0 0.0 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showstringspaces=false, + showtabs=false, + tabsize=2 +} +\lstset{style=mystyle} +\def\@maketitle{% + \newpage + \null + \vskip 2em% + \begin{center}% + \let \footnote \thanks + {\LARGE \@title \par}% + \vskip 1.5em% + {\large + \lineskip .5em% + \begin{tabular}[t]{c}% <------ + \@author% <------ Authors + \end{tabular}\par}% <------ + \vskip 1em% + {\large \@date}% + \end{center}% + \par + \vskip 1.5em} +%opening +\newcommand{\snovdn}{Kemijsko ravnotežje in vplivi na kemijsko ravnotežje } +\newcommand{\predmdn}{kem} +\newcommand{\predmkaj}{vaje} +\newcommand{\stevilkadn}{2} +\newcommand{\cm}[1]{\SI{#1}{\centi\meter}} +\newcommand{\kmh}[1]{\SI{#1}{\kilo\meter\per\hour}} +\makeatletter +\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname} +\newcommand{\@xslalph}[1]{% + \ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i% + \or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}% + \or t\or u\or v\or z\or \v{z} + \else\@ctrerr\fi% +} +\AddEnumerateCounter{\xslalph}{\@xslalph}{m} +\makeatother +\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma +\newcommand*\textfrac[2]{ + \frac{\text{#1}}{\text{#2}} +} +\NewTasks[counter-format=\xslalph*),label-format=\bfseries]{primerTasks}(3) +\newcommand\vektor{\overrightarrow} +\newcommand{\iic}{I\textsuperscript{2}C } +\title{% + \snovdn --- \stevilkadn. vaja + \\ + \large Kemija, Gimnazija Bežigrad} +\author{\begin{tabular}{rl} + \textbf{Profesor:} & prof. Gašper Pernek\\ + \textbf{Avtor:} & Anton Luka Šijanec, 2. a +% \textbf{Avtor:} & Anton Luka Šijanec \\ & Member 2 \\ & Member 3 +\end{tabular}} +\newcommand\hcancel[2][black]{\setbox0=\hbox{$#2$}% +\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2} +% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260 +\begin{document} +\maketitle +\begin{abstract} +Ta dokument vsebuje vajo, ki zajema snov \textit{\snovdn}pri kemiji. +\end{abstract} +\tableofcontents +\section{Pregledne naloge: \textit{\snovdn}} +\begin{enumerate}[label=\textbf{\arabic*.}] + \item Sliki prikazujeta stanje pred reakcijo in ravnotežno stanje. + \begin{figure}[H] + \centering + \includegraphics[width=0.7\textwidth]{1.png} + \caption{Vir slike: profesor} + \end{figure} + \begin{enumerate}[label=\xslalph*)] + \item Zapiši urejeno enačbo reakcije z agregatnimi stanji, ki poteče. + $$\ch{2 CO(g) + O2(g) <=> 2 CO2(g)}$$ + \item Zapiši izraz za konstanto ravnotežja in izračunaj njeno vrednost, če predpostavimo, da vsak model molekule v \SI{1,4}{\L} posodi predstavlja množino \SI{0,025}{\mole}. + $$K_c=\frac{[\ch{CO2}]^2}{[\ch{CO}]^2\cdot[O]}=\frac{0,0013}{0,000358}=3,6$$ + \end{enumerate} + \item Vrednost konstante ravnotežja za prikazano reakcijo je 0,0245. + $$\ch{2 NOCl(g) <=> 2 NO(g) + CL2(g)}$$ + Zapiši izraz za ravnotežno konstanto in izračunaj njeno vrednost za spodnji reakciji: + + \begin{tabular}{cc} + $$\ch{NOCl(g) <=> NO(g) + 1/2 CL2(g)}$$ & $$K_c = 0,16$$\\ + $$\ch{2 NO(g) + Cl2(g) <=> 2 NOCl(g)}$$ & $$K_c = 40,8$$ + \end{tabular} + \item Prikazani so štirje grafi spreminjanja koncentracije reaktantov A in B ter produktov C in D v odvisnosti od časa pri različnih pogojih. Kateri graf ustreza reakciji z največjo konstanto ravnotežja $K_c$? + \begin{figure}[H] + \centering + \includegraphics[width=0.9\textwidth]{3.png} + \caption{Vir slike: profesor} + \end{figure} + Največja konstanta ravnotežja $K_c$ pripada grafu 2. + Najmanjša konstanta ravnotežja $K_c$ pripada grafu 4, ker je tam koncentracija reaktantov najbolj različna od koncentracije produktov. + \item Prikazan je diagram spremembe koncentracij v odvisnosti od časa pri ravnotežni reakciji. Ali izraz za konstanto ravnotežja ustreza reakciji, prikazani na grafu? Vse snovi so plini. Utemelji. + \begin{multicols}{2} + \begin{figure}[H] + \centering + \includegraphics[width=0.4\textwidth]{4.png} + \caption{Vir slike: profesor} + \end{figure} + $$K_c=\frac{[\ch{SO2}]^2\cdot[\ch{O2}]}{[\ch{SO3}]^2}$$ + Ne, ne ustreza, ker morajo biti reaktanti napisani v števcu, tukajle pa so v imenovalcu. + Zapiši enačbo reakcije homogenega ravnotežja, ki jo prikazuje graf: + $$\ch{2 SO2(g) + O2(g) <=> 2 SO3(g)}$$ + \end{multicols} + Kakšen bi bil izraz za konstanto ravnotežja, če bi žveplov trioksid \ch{SO3} bil v trdnem agregatnem stanju? + $$K_c=\frac{1}{[\ch{SO2}]^2\cdot[\ch{O2}]}$$ + \item Metanol dobimo pri ravnotežni homogeni reakciji med ogljikovim oksidom in vodikom po enačbi \ch{CO(g) + 2 H2(g) <=> CH3OH(g)}. Pri določenih pogojih smo v posodi s prostornino \SI{900}{\milli\L} imeli na začetku \SI{0,345}{\mole} ogljikovega oksida in \SI{0,678}{\mole} vodika, v ravnotežju pa \SI{0,045}{\mol} metanola. Izračunaj ravnotežne koncentracije vseh snovi in konstanto ravnotežja $K_c$. + + \begin{tabular}{c||c|c|c} + & \ch{CO} & \ch{H2} & \ch{CH3OH} \\ + \hline + začetek & 0,38 M & 0,75 M & 0 \\ + \hline + potek & $-x$ & $-2x$ & $+x$ \\ + \hline + konec & 0,33 M & 0,65 M & 0,05 M + \end{tabular} + + $$x=0,05 \text{M}$$ + % $$C_r(\ch{CO}=0,33 \text{M});\ C_r(\ch{H2})=0,64 \text{M};\ C_r(\ch{CH3OH})=0,05 \text{M}$$ + $$[\ch{CO}]=0,33 \text{M}\ [\ch{H2}]=0,64 \text{M}\ [\ch{CH3OH}]=0,05 \text{M}\ K_c=0,36$$ + \item Dušikov(IV) oksid pridobivamo z reakcijo med kisikom in dušikovim(II) oksidom. + \begin{enumerate}[label=\xslalph*)] + \item Zapišite urejeno enačbo reakcije nastanka dušikovega(IV) oksida. + $$\ch{2 NO(g) + O2(g) <=> NO2(g)}$$ + \item Pri neki temperaturi ima konstanta ravnotežja $K_c$ vrednost 0,456. Izračunajte \textbf{ravnotežno koncentracijo} in \textbf{maso} kisika, če imamo v ravnotežju v \SI{750}{\milli\L} posodi \SI{0,500}{\mole} dušikovega(II) oksida in \SI{0,100}{\mole} dušikovega(IV) oksida. + $$ + C_R(\ch{NO})=0,67 \text{M};\ C_R(\ch{NO2})=0,13 \text{M};\ + K_c=\frac{[\ch{NO2}]^2}{[\ch{O2}]\cdot[\ch{NO}]^2};\ + C_R(\ch{O2})=\frac{[\ch{NO2}]^2}{K_c\cdot[\ch{NO}]^2};\ + C_R(\ch{O2})=0,083 \text{M} + $$ + \end{enumerate} + $$[\ch{O2}]=0,083 \text{M}\ m(\ch{O2})_R=\SI{0,9}{\gram}$$ + \item Zapisana enačba opisuje kemijsko reakcijo sinteze metanola \ch{CH3OH}. Ugotovite vplive na položaj ravnotežja. \textbf{\ch{CO(g) + 2 H2(g) <=> CH3OH(g)}}\ \ \ $\Delta H_r^\circ=\SI{-91}{\kilo\joule}$ + + \begin{tabular}{|c|c|} + \hline + \textbf{DEJAVNIK VPLIVA} & \textbf{VPLIV NA RAVNOTEŽJE} \\ + \hline + \textbf{Sistemu povišamo temperaturo.} & V levo \\ + \hline + \textbf{Sistemu povečamo tlak.} & V desno \\ + \hline + \textbf{Dodamo dodatno količino ogljikovega oksida.} & V desno \\ + \hline + \textbf{Odvzamemo neko količino metanola} & V desno \\ + \hline + \textbf{Dodamo \SI{0,5}{\mole\per\L} argona.} & Ni vpliva \\ + \hline + \end{tabular} + \item Pri endotermni ravnotežni reakciji, ki jo ponazarja spodnja enačba, lahko spremembo položaja ravnotežja opazimo s spremembo barve raztopine. + $$\ch{[Co(H2O)6]^{2+}(aq) + 4 Cl^-(aq) <=> [CoCl4]^{2-}(aq) + 6 H2O(l)}$$ + Reaktanti so \color{magenta}rožnate barve\color{black}, produkti pa \color{blue}plave barve\color{black}. + + Katere ugotovitve so pravilne za to reakcijo? + \begin{enumerate}[label=\textbf{\MakeUppercase{\alph*}}] + \item Ob dodatku koncentrirane klorovodikove kisline se raztopina obarva modro. + \item Če dodamo trden \ch{CoCl2}, ki tvori \ch{[Co(H2O)6]}, se ravnotežje pomakne k produktom. + \item Če raztopino segrejemo, opazimo prehod iz modre v rožnato barvo. + \item Segrevanje ne vpliva na položaj ravnotežja. + \item Ob dodatku vode se bo raztopina obarvala rožnato. + \end{enumerate} + Kombinacija pravilnih trditev: A, B in E + \item Dana je enačba ravnotežne kemijske reakcije med ogljikovim oksidom in vodikom. Pri \SI{1200}{\degreeCelsius} je konstanta ravnotežja za to reakcijo $K_c=9,17\cdot10^{-2}$. Katera trditev je pravilna? + \begin{enumerate}[label=\textbf{\MakeUppercase{\alph*}}] + \item V ravnotežni zmesi pri \SI{1200}{\degreeCelsius} prevladujejo produkti. + \item Če bi znižali temperaturo v reakcijski posodi, bi se konstanta ravnotežja povečala. + \item Dodatek vodika v posodo pri \SI{1200}{\degreeCelsius} ne bi vplicval na ravnotežne koncentracije produktov. + \item Povečanje tlaka v reakcijski posodi bi ravnotežje reakcije usmerilo proti levi. + \end{enumerate} + Pravilna trditev: B + \item Za zapisano reakcijo je pri določenih pogojih vrednost ravnotežje konstante $K_c=0,785$. + $$\ch{N2O4(g) <=> 2xNO2(g)}$$ + \begin{enumerate}[label=\alph*)] + \item Kolikšna je ravnotežna koncentracija dušikovega dioksida, če imamo bv ravnotežju \SI{0,234}{\mole\per\L} didušikovega tetraoksida? + $$K_c=\frac{[\ch{NO2}]^2}{[\ch{N2O4}]};\ [\ch{NO2}]=\sqrt{K_c\cdot[\ch{N2O4}]}=0,43 \text{M}$$ + \item Graf prikazuje potek te reakcije --- spreminjanje koncentracij v odvisnosti od časa. + \begin{figure}[H] + \centering + \includegraphics[width=0.5\textwidth]{10.png} + \caption{Vir slike: profesor} + \end{figure} + \end{enumerate} + \begin{enumerate}[label=\textbf{\MakeUppercase{\alph*}.}] + \item Kako smo vplivali na ravnotežje ob času $t_1$? + + Z zmanjšanjem tlaka ali s segrevanjem. + \item Kako smo vplivali na ravnotežje ob času $t_3$? + + Z dodajanjem \ch{NO2}. + \item Izračunaj konstanto ravnotežja med $t_2$ in $t_3$. + + 1,8. + \end{enumerate} +\end{enumerate} +\section{Zaključek} +Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in +\hologo{LaTeX}\footnote{Za izdelavo dokumenta potrebujete \texttt{TeXLive 2020}.} +izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo v mojem šolskem Git repozitoriju na +\url{https://git.sijanec.eu/sijanec/sola-gimb-2} v mapi +\href{https://git.sijanec/sola-gimb-2/src/branch/master/\predmdn/\predmkaj/\stevilkadn/}{/\predmdn/\predmkaj/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/\predmkaj/\stevilkadn/dokument.pdf} in/ali \url{https://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/master/\predmdn/\predmkaj/\stevilkadn/dokument.pdf}. + +\if\razhroscevanje1 +\section*{Razhroščevalne informacije} +Te informacije so generirane, ker je omogočeno razhroščevanje. Pred objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroscevanje} na 0 v začetku dokumenta. + +Grafi imajo natančnost \functionSamples\space točk na graf. + +Konec generiranja dokumenta: \today\ ob \currenttime\footnote{To ne nakazuje dejanskega časa, ko je bil dokument napisan, temveč čas, ko je bi dokument generiran v PDF/DVI obliko. Isto velja za datum v glavi dokumenta. Če berete direktno iz LaTeX datoteke, bo to vedno današnji datum.}%\input|"date -Ins" + +Dokument se je generiral R0qK1KR2 \SI{}{\second}. +\fi +% \item $$$$ aaasecgeninsaaa R0qK1KR2 +\end{document} diff --git a/kem/vaje/2/dokument.toc b/kem/vaje/2/dokument.toc new file mode 100644 index 0000000..1dfdf3d --- /dev/null +++ b/kem/vaje/2/dokument.toc @@ -0,0 +1,4 @@ +\babel@toc {slovene}{} +\babel@toc {slovene}{} +\contentsline {section}{\numberline {1}Pregledne naloge: \textit {Kemijsko ravnotežje in vplivi na kemijsko ravnotežje }}{1}{section.1}% +\contentsline {section}{\numberline {2}Zaključek}{4}{section.2}% diff --git a/kem/vaje/2/stderr.log b/kem/vaje/2/stderr.log new file mode 100644 index 0000000..e69de29 diff --git a/kem/vaje/2/stdout.log b/kem/vaje/2/stdout.log new file mode 100644 index 0000000..50316c3 --- /dev/null +++ b/kem/vaje/2/stdout.log @@ -0,0 +1,436 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020) (preloaded format=pdflatex) + \write18 enabled. 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1697 +Reading 196 0 R +Reading 197 0 R +Reading 198 0 R +Reading 199 0 R +Reading 200 0 R +Reading 201 0 R +Reading 202 0 R +Reading 203 0 R +Reading 204 0 R +Reading 205 0 R +Reading 206 0 R +Reading 207 0 R +Reading 208 0 R +Reading 209 0 R +Reading 210 0 R +Reading 211 0 R +Reading 212 0 R +-> Uncompressing object 212 0 +-> Original Length: 561 +-> Uncompressed Length: 1065 +/home/a/Documents/sola-gimb-2/kem/vaje/2/dokument.pdf was successfully uncompressed to: /home/a/Documents/sola-gimb-2/kem/vaje/2/dokument-uncompressed.pdf + **** Error: An error occurred while reading an XREF table. + **** The file has been damaged. This may have been caused + **** by a problem while converting or transfering the file. + **** Ghostscript will attempt to recover the data. + **** However, the output may be incorrect. + **** Error: stream Length incorrect. + Output may be incorrect. diff --git a/nem/hausaufgabe/9/dokument.md b/nem/hausaufgabe/9/dokument.md new file mode 100644 index 0000000..9b07fd6 --- /dev/null +++ b/nem/hausaufgabe/9/dokument.md @@ -0,0 +1,44 @@ +Wechselspiel +=========== + +# 10 Sätze / Dialoge + +* Weißt du, was Manfred seinen Eltern schenkt? +* *Ich glaube, er schenkt ihnen ein Buch.* +* Aha, ja, er schenkt es ihnen. + +* Weißt du, was Sabine ihrem Freund schenkt? +* *Ich glaube, sie schenkt ihm Rasierwasser.* +* Aha, ja, sie schenkt sie ihm. + +* Weißt du, was Rolf seine Freundin schenkt? +* *Ich glaube, er schenkt ihr ein Kleid.* +* Aha, ja, er schenkt es ihr. + +* Weißt du, was Heinz seine Schwester schenkt? +* *Ich glaube, er schenkt ihr einen Briefpapier.* +* Aha, ja, er schenkt er ihr. + +* Weißt du, was Michael seinem Bruder schenkt? +* *Ich glaube, er schenkt ihm ein Hemd.* +* Aha, ja, er schenkt es ihm. + +* Weißt du, was Antje seinen Nachbarn schenkt? +* *Ich glaube, er schenkt ihnen nichts* +* Aha, ja, er schenkt nichts ihnen. + +* Weißt du, was Reiner seinen Eltern schenkt? +* *Ich glaube, er schenkt ihnen einen Teppich.* +* Aha, ja, er schenkt er ihnen. + +* Weißt du, was Brigitte ihrem Freund schenkt? +* *Ich glaube, sie schenkt ihm eine Uhr.* +* Aha, ja, sie schenkt ihm sie. + +* Weißt du, was Ich schenke meiner Freundin? +* *Ich glaube, du schenkst ihr Pralinen.* +* Aha, ja, Ich schenke ihr sie. + +* Was schenken Sie Ihrer Schwester? +* *Ich glaube, Ich schenke ihr einen Schal.* +* Aha, ja, schenken Sie er. diff --git a/ru/kolo/api.php b/ru/kolo/api.php index c085435..64dd35c 100644 --- a/ru/kolo/api.php +++ b/ru/kolo/api.php @@ -4,46 +4,155 @@ $dbhost = "localhost"; $dbdb = "kolo"; $dbpw = "kolo"; + $conn = new mysqli($dbhost, $dbuser, $dbpw, $dbdb); header("Content-Type: application/json"); + if ($conn->connect_error) { + http_response_code(500); + exit('{"napaka":true,"obvestilo":"Napaka strežnika pri povezavi v podatkovno zbirko."}'); + } + $query = "CREATE TABLE IF NOT EXISTS kolesa ( + omogoceno INT, + ime VARCHAR(420), + admin VARCHAR(420) + ); + CREATE TABLE IF NOT EXISTS ljudje ( + ime VARCHAR(420) PRIMARY KEY, + izbranec VARCHAR(420), + kolo VARCHAR(420), + krneki VARCHAR(420) + )"; + $result = $conn->query($query); + var_dump($result); + var_dump($conn->error); if (empty($_REQUEST['k'])) { http_response_code(400); exit ('{"napaka":true,"obvestilo":"Ne vem, na katero kolo se sklicuješ, ker manjka parameter k."}'); } switch ($_REQUEST['m']) { case "r": /* registracija */ - if (empty($_REQUEST['m'])) { + if (empty($_REQUEST['i'])) { + http_response_code(400); + exit ('{"napaka":true,"obvestilo":"Ne vem, kako ti je ime, ker manjka parameter i"}'); + } + $stmt2 = $conn->prepare("SELECT omogoceno FROM `kolesa` WHERE `ime`=?"); + $stmt2->bind_param("s", $_REQUEST["k"]); + $stmt2->execute(); + $stmt2->bind_result($omogoceno); + $stmt2->fetch(); + if ($omogoceno != 0) { http_response_code(400); - exit ('{"napaka":true,"obvestilo":"Ne vem, kako ti je ime, ker manjka parameter m"}'); + exit ('{"napaka":true,"obvestilo":"Ne morem registrirati novih ljudi, ker se je vrtenje koles že začelo.}'); } - /* sedaj naredimo SQL */ + $stmt2->close(); + $stmt = $conn->prepare("INSERT INTO ljudje (ime, kolo) VALUES (?, ?) ON DUPLICATE KEY UPDATE `krneki`='123'"); + $stmt->bind_param("ss", $_REQUEST["i"], $_REQUEST["k"]); + $stmt->execute(); + $stmt->close(); + http_response_code(201); + exit ('{"napaka":false,"obvestilo":"Uporabnik registriran!"}'); break; case "z": /* zakleni kolo, omogoči vrtenje, naključno razporedi osebe */ + $stmt = $conn->prepare("SELECT admin FROM kolesa WHERE `ime`='?'"); + $stmt->bind_param("s", $_REQUEST["k"]); + $stmt->execute(); + $stmt->bind_result($admin_pass); + $stmt->fetch(); if ($_REQUEST['g'] !== $admin_pass) { http_response_code(400); exit ('{"napaka":true,"obvestilo":"Ne bom zaklenil tega kolesa, ker niste administrator."}'); } + $stmt->close(); + $stmt = $conn->prepare("UPDATE kolesa SET `omogoceno`=1 WHERE `ime` = '?'"); + $stmt->bind_param("s", $_REQUEST["k"]); + $stmt->execute(); + $stmt->close(); + $stmt2 = $conn->prepare("SELECT ime FROM ljudje WHERE `kolo`=?"); + $stmt2->bind_param("s", $_REQUEST["k"]); + $stmt2->execute(); + $result = $stmt->get_result(); + $ljudje = $result->fetch_all(MYSQLI_ASSOC); + $ljudje2 = $ljudje; + shuffle($ljudje); + for ($i = 0; $i < sizeof($ljudje);) { + if ($ljudje[$i] == $ljudje2[$i]) { + shuffle($ljudje); + $i = 0; + continue; + } + $i++; + } + $stmt3 = $conn->prepare("UPDATE ljudje SET `izbranec`=? WHERE `ime`=?"); + for ($i = 0; $i < sizeof($ljudje); $i++) { + $stmt3->bind_param("ss", $ljudje[$i], $ljudje2[$i]); + $stmt3->execute(); + } + $stmt3->close(); + $stmt2->close(); + http_response_code(200); + exit ('{"napaka":false,"obvestilo":"uspešno zaklenil kolo."}'); break; case "u": /* srčni utrip */ $r = array(); - $r["dovoli_vrtenje"] = false; - $r["si_administrator"] = false; - $r["moznosti_na_kolesu"] = false; + $stmt2 = $conn->prepare("SELECT ime FROM ljudje WHERE `kolo`=?"); + $stmt2->bind_param("s", $_REQUEST["k"]); + $stmt2->execute(); + $result = $stmt->get_result(); + $ljudje = $result->fetch_all(MYSQLI_ASSOC); + $r["moznosti_na_kolesu"] = $ljudje; + $stmt = $conn->prepare("SELECT admin FROM kolesa WHERE `ime`=?"); + $stmt->bind_param("s", $_REQUEST["k"]); + $stmt->execute(); + $stmt->bind_result($admin_pass); + $stmt->fetch(); + if ($admin_pass === $_REQUEST["g"]) { + $r["si_administrator"] = true; + } else { + $r["si_administrator"] = false; + $r["si_administrator"] = false; + } + $stmt3 = $conn->prepare("SELECT omogoceno FROM `kolesa` WHERE `ime` = ?"); + $stmt3->bind_param("s", $_REQUEST["k"]); + $stmt3->execute(); + $stmt3->bind_result($omogoceno); + $stmt3->fetch(); + if ($omogoceno !== 1) { + $r["dovoli_vrtenje"] = false; + } else { + $r["dovoli_vrtenje"] = true; + } + $r["napaka"] = false; + $stmt2->close(); + $stmt->close(); + $stmt3->close(); http_response_code(200); exit (json_encode($r)); break; case "v": /* vrti */ - if (true /* a je vrtenje nedovoljeno */) { + $stmt3 = $conn->prepare("SELECT omogoceno FROM `kolesa` WHERE `ime` = ?"); + $stmt3->bind_param("s", $_REQUEST["k"]); + $stmt3->execute(); + $stmt3->bind_result($omogoceno); + $stmt3->fetch(); + if ($omogoceno !== 1 /* a je vrtenje nedovoljeno */) { http_response_code(400); exit ('{"napaka":true,"obvestilo":"Ne morem vrteti, ker vrtenja še ni odobril administrator"}'); } - if (true /* če je uporabnik že zavrtel kolo */) { + if (empty($_REQUEST["i"])) { http_response_code(400); - exit ('{"napaka":true,"obvestilo":"Kolesa ne morem vrteti, ker ste ga enkrat že zavrteli."}'); + exit ('{"napaka":true,"obvestilo":"Ne morem vrteti, ker nimam vašega imena."}'); } - /* pridobi obstoječo vrednost iz tabele in jo označi za taken */ + $stmt2 = $conn->prepare("SELECT izbranec FROM `ljudje` WHERE `ime` = ?"); + $stmt2->bind_param("s", $_REQUEST["i"]); + $stmt2->execute(); + $stmt2->bind_result($izbranec); + $stmt2->fetch(); + $r["izbranec"] = $izbranec; + $r["napaka"] = false; + $stmt3->close(); + $stmt2->close(); http_response_code(200); - exit (); + exit(json_encode($r)); break; default: http_response_code(400); -- cgit v1.2.3 From e55ed55a1920ba68b87dc9f0ea3c8da374086657 Mon Sep 17 00:00:00 2001 From: sijanec Date: Tue, 22 Dec 2020 16:54:06 +0100 Subject: =?UTF-8?q?za=20vsak=20slu=C4=8Daj,=20izbrisan=20fajl=20bi=20pomen?= =?UTF-8?q?il=20izbris=20"znanja"=20zgodovine?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- zgo/ocena/1/dokument.md | 61 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 61 insertions(+) create mode 100644 zgo/ocena/1/dokument.md diff --git a/zgo/ocena/1/dokument.md b/zgo/ocena/1/dokument.md new file mode 100644 index 0000000..65ea8bb --- /dev/null +++ b/zgo/ocena/1/dokument.md @@ -0,0 +1,61 @@ +Prvo spraševanje zgodovine. +=========================== + +# Rim + +## Propad imperija + +* kriza po 200 letnem obdobju miru v 3. stoletju - rast kriminala, izguba moči senata, vdor tujih ljudstev + - vzroki: življenje na tuj račun, veliko sužnjev imajo obrtniki, šibko gospodarstvo, slaba družba +* vladarji, ki so reševali krizo: + - 212: Karakala: Zakon o državljanstvu za svobodne prebivalce provinc - priseljenci in najemniki dobijo drž. => problem s tujci + - 284-305: Dioklecijan: za 200 let vzpostavi mir - vojaške, finančne, upravne reforme; razdelitev države - + tetrarhija: dva vladarja, dva namestnika, dominat: ni več senata, vladal je sam, 301 je pregnal kristjane. + ga ne ubijejo. 305: rim oslabi, Dioklecijan odstopi + - 307-337: Konstantin: nadaljne reforme, prenese prestolnico v Konstantinopelj/Car./Ist., Milanski edikt: ne preganja več kristja. + - 379-395: Teodozij: Uspešen vojskovodja, cesar [V] rima, v [Z] tetrarhije in hitre menjave, zadnjič združi Rimski imperij + + po smrti 395 razpade Rim, bitka pri Frigidu: Teodozij proti Evgeniju (pogan) - zmaga krščanstva na naših tleh. +* 395 meja Rima: Beograd-Kotor-zaliv velike Sirte v [S] afriki. + - [V]: še 1000 letni obstoj, 1453 ga zasedejo Turki, središče Konstantinopelj, bolj gospodarsko razvit, ne preganjajo raznih ver + - [Z]: 476 Goti odstavijo zadnjega cesarja Romula Avgustula in za kralja postavijo Odoakerja-konec rimskega cesarstva->sredni vek + +### Vzroki za propad + +* Vpad tujih ljudstev: tarča napadov, Kelti/Germani 4. st., Langobardi/Markomani druga polovica 2. st., + Germani(Goti, Vandali, Langobardi) & nomadi(Huni, Alani) v 5. stoletju; šibka vlada +* Demografski razlogi: Št. prebivalcev se zmanjša, Germane sprejmejo kot vojsko, hiperinflacija: ni denarja, vojakom dajo ozemlje. +* Gospodarska/ekonomska kriza: gospodarstvo v razsulu, izkoriščajo naravna bogastva provinc in sužnjev, visoki davki, + razkošno življenje cesarjev, imperij se ne širi več-ni sužnjev/denarja/hrane, samo blagovna menjava + - kolonata/zakupništvo v 3. stoletju: oblika zgodnjih fevdalnih odnosov, oddaš zemljo v zameno za 1/3 pridelka v obdelavo. +* šibkost centralne oblasti: slabi odnosi cerkev-senat-vojska, dedni princip; raste vpliv vojske +* tuji najemniki v vojski: vojska hoče več od bogatih in ne obrani ljudstva pred barbari. +* duhovna kriza: vere iz [V]: mitraizem in krščanstvo zamenjata politeizem, namesto prednikov spoštujejo samo še boga. + - kruha in iger: državljani postanejo apatični in leni + +## Priseljevanje ljudstev (4.-7. stoletje) + +* Huni, Germani, Obri/Avari, Slovani +* Pavel Diakom "Rimska zgodovina - *historia romana*" (pred 774/njegovo smrtjo), piše o bitki pri Frigidu 300-400 let po njej + - najbolj krvava bitka na SLO, Vipava polna trupel, Teodozij poln vere sam plane v vojno, zmaga zaradi vetra, Evgenij pokončan. +* Vzroki za preseljevanje: pomanjkanje hrane, preprosto življenje, mika jih bogastvo Rima, medplemenski spopadi, pritiski tujih + ljudstev, želja po zasedbi ozemelj, prenaseljenost. +* Preseljevalci: Germani, Slovani, Arabci, Huni (vzrok za Germane), Obri/Avari v 6. st. (vzrok za Slovane) + +### Huni + +* arijsko-nomadsko/stepsko ljudstvo začne preseljevanje na Kitajsko, a tam zgradijo Kitajski zid (brah moment) +* središče na dan. Madžarskem, pritiskajo na Germane, dobri jezdeci, 100km/dan, lokostrelci (iz konja zadene 60m cilj), nomadsko lj. +* Vrhunec: 4. st.: Atita (406-453 "bič božji") združi hune dan. Nemčije, panonske nižine, Kaspijskega J., Laponske (Z,J,V,S) + - [V] Rim mu za nenapadanje plačuje letni davek/TRIBUT. 451 ga na Katalonskem polju v Grčiji premaga zdru. vojs. Rima in Vizigotov +* Huni slovensko ozemlje dosežejo 451 in ga plenijo 452. + +### Germani + +* Rimljani jih imajo zaradi neciviliziranega jezika za barbare. Germanska pradomovina je v [J] skandinaviji. +* 1. st.: naselitev na ozemlje med Renom in Odro. Obrt in živinoreja na stopnji rodovno plemenskih zvez in so razslojeni. +* Kralji, vojaške aristokracije, politeizem - Doin, Thor, Freya. Vojskovanje: Frančiška-bojna sekira za met in šilasti meči +* služili v Rimski vojski kot federati. +* [Z] Goti: Leta 410 prvič dobijo Rim, naselijo se v bližino črnega morja. 375 zbežijo pred Huni na ozemlje [V] rimskega cesarstva. + - se sprejo z vladarjem => [S] Grčija => Ilirik in Novik (rimski provinci) => 401 vdrejo v Italijo, 410 zasedejo in izropajo RIM. + - =x neuspešen prodor na Sicilijo => naselitev v galijo - tam so že franki => Pirenejski polotok - dokončna naselitev +* Runska Pisava: 1. st., ravne črte, kombinacija grške in latinske, izum Keltov -- cgit v1.2.3 From b6eeb3822ff2518b11c88d81475508a0e05af64c Mon Sep 17 00:00:00 2001 From: sijanec Date: Tue, 22 Dec 2020 17:53:04 +0100 Subject: =?UTF-8?q?za=20vsak=20slu=C4=8Daj?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- zgo/ocena/1/dokument.md | 50 ++++++++++++++++++++++++++++++++++++++++++++++--- 1 file changed, 47 insertions(+), 3 deletions(-) diff --git a/zgo/ocena/1/dokument.md b/zgo/ocena/1/dokument.md index 65ea8bb..8bc2ddf 100644 --- a/zgo/ocena/1/dokument.md +++ b/zgo/ocena/1/dokument.md @@ -11,7 +11,7 @@ Prvo spraševanje zgodovine. - 212: Karakala: Zakon o državljanstvu za svobodne prebivalce provinc - priseljenci in najemniki dobijo drž. => problem s tujci - 284-305: Dioklecijan: za 200 let vzpostavi mir - vojaške, finančne, upravne reforme; razdelitev države - tetrarhija: dva vladarja, dva namestnika, dominat: ni več senata, vladal je sam, 301 je pregnal kristjane. - ga ne ubijejo. 305: rim oslabi, Dioklecijan odstopi + ga ne ubijejo. 305: rim oslabi, Dioklecijan odstopi. Dioklecijan je bil sin sužnja. - 307-337: Konstantin: nadaljne reforme, prenese prestolnico v Konstantinopelj/Car./Ist., Milanski edikt: ne preganja več kristja. - 379-395: Teodozij: Uspešen vojskovodja, cesar [V] rima, v [Z] tetrarhije in hitre menjave, zadnjič združi Rimski imperij + po smrti 395 razpade Rim, bitka pri Frigidu: Teodozij proti Evgeniju (pogan) - zmaga krščanstva na naših tleh. @@ -57,5 +57,49 @@ Prvo spraševanje zgodovine. * služili v Rimski vojski kot federati. * [Z] Goti: Leta 410 prvič dobijo Rim, naselijo se v bližino črnega morja. 375 zbežijo pred Huni na ozemlje [V] rimskega cesarstva. - se sprejo z vladarjem => [S] Grčija => Ilirik in Novik (rimski provinci) => 401 vdrejo v Italijo, 410 zasedejo in izropajo RIM. - - =x neuspešen prodor na Sicilijo => naselitev v galijo - tam so že franki => Pirenejski polotok - dokončna naselitev -* Runska Pisava: 1. st., ravne črte, kombinacija grške in latinske, izum Keltov + - =x neuspešen prodor na Sicilijo => naselitev v galijo - franki => Pirenejski polotok - dokončna naselitev +* Runska Pisava: 1. st., ravne črte, kombinacija grške in latinske, izum Keltov, vkles v kamen na danskem. + - zapis prava: Rotharijev edikt pri Langobardih (643) in Julijski zakon pri frankih (6. st.) +* zapustijo politeizem za krščanstvo, za rimljane krivoverci. +* Germanska plemena (300). Goti se po 3. st. razdeliko na VIZIGOTE ([V] Goti, španija in [J] francija) in OSTROGOTE ([Z] G, italija) + - FRANKI, BURGUNDI: [JV] fr, VANDALI: špa, [S] afrika, ALEMANI, BAVARCI: [S] Alpe, ALANI, SVEBI: Apenin. pol., ANGLI/SASI/JUTI:ANG + +### Slovani + +* Pradomovina: porečje treh rek: Dnjeper, Dnjester, Visla. Etimologija imena ni povsem pojasnjena. Na nižji stopnji razvitosti. +* Poljedelstvo, živinoreja - rodovska skupnost - nižje od Germanov, skromna bivališča - ZEMLJANKE +* naselitev na izpraznjena območja Germanov, izbezajo jih Obri ali Avari. +* Več bogov: Morana-smrt, Vesna-pomlad, Svarog-ogenj, Perun-grom +* skupine: [V]: rusi, belorusi, ukrajinci; [J]: srbi, črnogorci, makedonci, hrvati; [Z]: poljaki, čehi, slovaki, lužiški srbi +* mi delno iz [S] in panon. niž. poselimo [V] Alpe. spadamo pod južne slovane, glede na smer preseljevanja. +* 6. st.: o nas in o veri piše bizantinski zgodovinar Prokopij. časimo reke, vile, divje plese, bodočnost, pojedine, petje +* tujci hvalijo slovansko gostoljubnost. mel smo tut kul žene pa to... i guess... + +### Avari ali Obri + +* azijsko-stepsko-nomadsko ljudstvo/plemenska zveza / naj bi obstajala obrsko-slovanska plemena +* 6. st.: vdrejo v Evropo. obri=konjeniki, slovani=pešaki/pešci, naseljio se v panonsko nižino, ko grejo [V] Goti v Italijo +* 561 z Langobardi uničijo državo Gepido. Ustanovitelj Kan Bajan-6. st. z bizantinci (Justinijan I.) sklene pogodbo o varovanju [S] +* 582: osvojijo Sremsko Mitrovico. + +### Bizantinska država ([V] Rim) in Justinijan + +* Ime države iz Bizanta (Istanbul/Carigrad/Konstantinopelj) +* cesar Justinijan 527-565: sin ilirskega kmeta, učena žena Teodora-uveljavi vseveljavno nadgrajeno [Z] rim. pravo-Justinij. zakonik + - neuspel pri poskusu združitve Rima, je pa ta kulturni vpliv občuten v Benetkah. hotel obnoviti moč [V]+[Z] + - vzroki za neuspeh: preseljevanja ljudstev, potrebna obramba pred [S] ljudstvi, pol. & ver. neenotnost: [Z]: latinščina/[V]: GR + - vojskovodji: BELIZAR in NARSES obnovita IT, AFR, [J] ŠPA; a se ljudstva uprejo. + + Langobardi vdrejo v Ita.-6. st., Arabci osvojijo Afriko-7. st., Španijo-8. st., Sicilijo-9. st. + - cerkev podredi državi-cezaropapizem, se upre vojski, uradništvu +* Bizantinsko cesarstvo: helenistična kultura, vpliv krščanske vere, rimskega prava +* kodeks justinjanus: manjši vpliv očeta na otroke, preganj. krivovercev, bolj svobodni sužnji, prepoved ločitve (ironic), trg z [Z] + +# frankovska država + +* senior zemljo da vazalu, medsebojne dolžnosti (fevdni odnosi) ali pa odvzem zemlje. vrhovni senior je vladar. +* tudi vazal je fevdalec, podložnik pa ni. nižje plemstvo nima fevdov/so premajhni. +* prej so bili začasni, v času karolingov postanejo fevdi dedni. +* zemljiško gospostvo: + - prirodna/dominikalna zemlja-bližina fevdalca: gosposki dvor: upravno/gospodarsko središče, stan. upravnika, gospoda, hlapcev + - zakupna/rustiklana zemlja/HUBA: dana podložnikom v zameno za dajatve in tlako na dominikalni zemlji, dovoljšna za eno družino +* 5.-10. st.: zgodnji, 11.-15. st.: razviti, 16.-18. st.: pozni fevdalizem -- cgit v1.2.3 From 7cf43b3ad62d5e1f6a805a4ba608f864cf3c9667 Mon Sep 17 00:00:00 2001 From: sijanec Date: Tue, 22 Dec 2020 18:46:31 +0100 Subject: =?UTF-8?q?=C5=A1e=20malo=20teksta=20zgodovine,=20more=20to=20come?= =?UTF-8?q?=20tho?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- zgo/ocena/1/dokument.md | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) diff --git a/zgo/ocena/1/dokument.md b/zgo/ocena/1/dokument.md index 8bc2ddf..7ef259d 100644 --- a/zgo/ocena/1/dokument.md +++ b/zgo/ocena/1/dokument.md @@ -103,3 +103,26 @@ Prvo spraševanje zgodovine. - prirodna/dominikalna zemlja-bližina fevdalca: gosposki dvor: upravno/gospodarsko središče, stan. upravnika, gospoda, hlapcev - zakupna/rustiklana zemlja/HUBA: dana podložnikom v zameno za dajatve in tlako na dominikalni zemlji, dovoljšna za eno družino * 5.-10. st.: zgodnji, 11.-15. st.: razviti, 16.-18. st.: pozni fevdalizem +* tlaka: izmerjena/določena (napovedana) ali neizmerjena/nedoločena (dodatna tlaka). podložnike obveznosti so v Z. K./urbarjih +* dajatve navadnim in cerkvenim fevdalcem: velika pravda-žito/vino, mala: izdelki/storitve, dajatve za javno upravo, 1/10 cerkvi + +# vzpon papeštva in nastanek cerkvene države + +* območje dan. IT, cerkvena organizacija sledi upravni org., patriarhat-škof/patriarh: Rim,Antiohija,Aleksandrija,Carigrad,Jeruzalem +* s prihodom Arabcev cerkvena organizacija na Bližnjem [V] in v [S] Afriki začne slabeti. +* razlike med rimskim in carigrajskim patriarhatom => 1054: dokončna delitev/SHIZMA na [Z] rimokatoliško in [V] pravoslavno cerkev. +* položaj papežov: ozemlje si pridobijo z darovi, zzapuščinami in zavezništvi + - rimski patriarh: voditelj skupnosti-papež. - papeška posest: patrimonij Sv. Petra. + - 529: menih Benedikt [J] od Rima na gori Monte Kasino: prvi samostan-Benediktinski-začetek krščanskega meništva-*ora et labora* + - Konstantinova darovnica: ponarejen cerkveni dokument, ki izkazuje lastništvo delov Italije +* shizma ali cerkveni razkol - najavljen že od ločitve rimskega cesarstva - ločitev cerkve na 2 dela - 11. st.: + - [V] pravoslavna <-> [Z] katoliška cerkev. dokončni razkol 1054: papež leon 9. na v cerkev Hagija-Sofija v Carigrad odnese + listino o izobčenju carigrajskega patriarha. to podpre zlom karolingov in kriza papeštva v 10. stoletju + - borba za moč in bogoslovna vprašanja: o celibatu in obredih + - rimsko cerkev v 11. st. obremenijo: SHIZMA in INVESTITURNI spor. + + OTON 1. saški (10.-11. st. / 919-1024) 926 ga Janez 12. okrona za cesarja, ima preveliko moč, izkoristi slabosti papeštva: + + se vmeša v zadeve Italije, papežu obljubi zaščito, vzajemni zaščitni odnos, lahko imenuje novega papeža in škofa (laična inv.) + + 1077: podobno se zgodi s papežem Gregorjem 7. in cesarjem Henrikom 4. +* cerkveni problemi 11. st., še enkrat - 1024 shizma(pravoslavna[V]|rimokatoliška[Z])=>papež ima manj moči + - investiturni boj med otonom I. saškim in rimskonemškim cesarjem, pravica do laične investiture + - ZAPLET: Gregor 7. in Henrik 4. -- cgit v1.2.3 From e597779a544fdd4965d36c7e771b79c96fbf51a2 Mon Sep 17 00:00:00 2001 From: sijanec Date: Tue, 22 Dec 2020 19:58:19 +0100 Subject: =?UTF-8?q?kri=C5=BEarske=20vojne=20in=20pape=C5=BEi=20pri=20u?= =?UTF-8?q?=C4=8Denju=20zgodovine?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- zgo/ocena/1/dokument.md | 27 ++++++++++++++++++++++++++- 1 file changed, 26 insertions(+), 1 deletion(-) diff --git a/zgo/ocena/1/dokument.md b/zgo/ocena/1/dokument.md index 7ef259d..a04b1b8 100644 --- a/zgo/ocena/1/dokument.md +++ b/zgo/ocena/1/dokument.md @@ -125,4 +125,29 @@ Prvo spraševanje zgodovine. + 1077: podobno se zgodi s papežem Gregorjem 7. in cesarjem Henrikom 4. * cerkveni problemi 11. st., še enkrat - 1024 shizma(pravoslavna[V]|rimokatoliška[Z])=>papež ima manj moči - investiturni boj med otonom I. saškim in rimskonemškim cesarjem, pravica do laične investiture - - ZAPLET: Gregor 7. in Henrik 4. + - ZAPLET: Gregor 7. (rimski papež) in Henrik 4. (rimskonemški cesar) + + henrik izkoristi pravico do investiture in ne želi potrditi papeža, doma ga podpirajo, 1077 se skuša opravičiti vrhovnemu pap. + + gre na pot odpuščanja v Kanoso (IT), papež mu po treh dneh čakanja zunaj na mrazu oprosti in prekliče izobčenje. + - 1122: Wormski konkordat - pogodba cerkev:država, zmagajo klinijske zahteve (Cluny-mesto s samostanom), zmaga menihov in papeštva + + trajna odprava laične investiture, uvedba celibata, prepoved simonije/prodaje cerkvenih služb, latinščina=edini jezik bogoslu. + +## križarske vojne (3. problem) + +* sredozemski prostor: različne vere: islam [V]-bizantinsko cesarstvo, krščanski [Z]. + - 11. st. v [J] franciji: mirovno gibanje TRUGA DEI zaradi fevdalskih spopadov cerkev vsak drugi teden prepove vojne da jih prepr. + - zaplet: romanja kristjanov v palestino ogrožajo muslimanski seldžuki (turkmensko ljudstvo). 1071 premagajo bizantince, ki so + papeža Urbana II. prosili za mir. ta dobi idejo za združitev krščanstvo. seldžuki 1077 zavzamejo jeruzalem, 1085 pa Antiohijo. + - Urban II. 1095 pozove na križarske vojne-pohod na sv. grob-križarjem odpusti vse grehe; vsi se udeležijo. + - križarske vojne trajajo 200 let, do 1209. +* 1. (1096-1099, zunanja kolonizacija): 4 skupine plemičev, kmetov&trgovcev neurejeno nasilno oblegajo jeruzalem (zastrupijo vode): + - križarji na [V] ustanovijo svoje države: Eldesa, Antiohija, Tripolui, Jeruzalemsko kraljestvo + - duhovno-viteški redovi-obramba pred muslim.: templarji po koncu=>FR&se ukvarjajo z denarjem, ivanovci/špitalarji, nemci=>prusija +* 2. povod: seldžujska osvojitev Edese 1144. džihad: sveta vojna proti nevernikom +* 3. Friderik Barbarosa (utone@prečkanje Salef), Filip II. Avgust, Rihard Levjesrčni (3 evr. vladarji). Zaradi zavzetja Jer. 1189-92 + - 1911 Filip II. Avgust in Richard Barbarosa zavzameta Ako. +* 4. 1202-1204: slabosti križ. vojn se pokažejo: benečani s prevozom edini zaslužijo, dobijo Zadar, svete dežele križ. ne dosežejo. +* Otroška (1215): tisoče 8-16 letnikov iz FR, otrokom so obljubljali dostojno življenje, na koncu jih prodajo kot sužnje arabcem. +* 5. križarska vojna in križarske vojne Sv. Ludvika: *nič znat* +* 6.: cesar in sultan si brez boja razdelita ozemlje, jeruzalemsko kraljestvo propade. +* Pomen in posledice - izrodijo se v dobičnokosne posle IT trgovcev in pustolovščin željnih fevdalcevi avanture, pregon poganov, + evropejci dobijo od razvitih arabcev kulturo, npr. umivanje rok, Italijanska mesta dobijo veliko denarja. -- cgit v1.2.3 From 51b435410c41197ee85f76c5310068dddd66a6c0 Mon Sep 17 00:00:00 2001 From: sijanec Date: Tue, 22 Dec 2020 20:33:49 +0100 Subject: =?UTF-8?q?zgo=20ocena=201:=20italijanske=20mestne=20dr=C5=BEavice?= =?UTF-8?q?=20in=20absolutizem?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- zgo/ocena/1/dokument.md | 35 ++++++++++++++++++++++++++++++++++- 1 file changed, 34 insertions(+), 1 deletion(-) diff --git a/zgo/ocena/1/dokument.md b/zgo/ocena/1/dokument.md index a04b1b8..fa4c5d8 100644 --- a/zgo/ocena/1/dokument.md +++ b/zgo/ocena/1/dokument.md @@ -18,6 +18,7 @@ Prvo spraševanje zgodovine. * 395 meja Rima: Beograd-Kotor-zaliv velike Sirte v [S] afriki. - [V]: še 1000 letni obstoj, 1453 ga zasedejo Turki, središče Konstantinopelj, bolj gospodarsko razvit, ne preganjajo raznih ver - [Z]: 476 Goti odstavijo zadnjega cesarja Romula Avgustula in za kralja postavijo Odoakerja-konec rimskega cesarstva->sredni vek + - na [V] območju nastane rimskonemško cesarstvo, na [Z] pa francija ### Vzroki za propad @@ -61,7 +62,7 @@ Prvo spraševanje zgodovine. * Runska Pisava: 1. st., ravne črte, kombinacija grške in latinske, izum Keltov, vkles v kamen na danskem. - zapis prava: Rotharijev edikt pri Langobardih (643) in Julijski zakon pri frankih (6. st.) * zapustijo politeizem za krščanstvo, za rimljane krivoverci. -* Germanska plemena (300). Goti se po 3. st. razdeliko na VIZIGOTE ([V] Goti, španija in [J] francija) in OSTROGOTE ([Z] G, italija) +* Germanska plemena (300). Goti se po 3. st. razdeliko na VIZIGOTE ([Z] Goti, španija in [J] francija) in OSTROGOTE ([V] G, italija) - FRANKI, BURGUNDI: [JV] fr, VANDALI: špa, [S] afrika, ALEMANI, BAVARCI: [S] Alpe, ALANI, SVEBI: Apenin. pol., ANGLI/SASI/JUTI:ANG ### Slovani @@ -151,3 +152,35 @@ Prvo spraševanje zgodovine. * 6.: cesar in sultan si brez boja razdelita ozemlje, jeruzalemsko kraljestvo propade. * Pomen in posledice - izrodijo se v dobičnokosne posle IT trgovcev in pustolovščin željnih fevdalcevi avanture, pregon poganov, evropejci dobijo od razvitih arabcev kulturo, npr. umivanje rok, Italijanska mesta dobijo veliko denarja. + +# Italijanske mestne državice + +* benetke - rimskonemško/svetorimsko cesarstvo - se osvobodijo - 3. največje mesto v Sr. veku: + - skupnost vodijo TRIBUNI: izbrani predstavniki teritorialno-vojaške aristokracije, nad njimi bizantinski vojvoda DUX/DOŽ + + da se prepreči korupcijo, ga ljudstvo voli. z razvojem plemstva se krepi povezava v VELIKI SVET +* ostala mesta: Genova, Pisa, Amalfi - močne pomorske sile; firence - tekstil +* meceni: financirajo učence, humanizem; diplomati, najemniške vojske + +# absolutizem + +* neomejena oblast človeka, poskus reševanja krize fevdalnega sistema +* oporo mu nudi uradništvo, davki, vojska, cerkev, centralizirana uprava; država ima velike finančne potrebe. +* prva absolutna monarhija: v španiji v 16. st. => močna država +* 10. st.: Kapetingi: šibka osrednja oblast, 13.-14. st.: vojna med anglijo in francijo (dinastija Valois) + - Hugenotske vojne v protireformacije in Dinastija Bourbonov - Ludvik XIV. / sončni kralj + - absolutizem vpeljeta kardinal Richelien in Mazarin. v klasičnem absolutizmu ni reform +* razsvetljeni absolutizem omogoča reforme in je kritičen do absolutizma, zadnji poskus ohranitve fevdalizma z reformami: + - FIZIOKRATIZEM: zemlja je sveta in ima edina novo vrednost, poudarek na kmetijstvu, z reformami se pomaga kmetom in 3. stanu. + - omilitev tlake, manj vpliva cerkve in plemstva +* Marija Terezija vlada 1740-1780 - PRAGMATIČNA SANKCIJA, PRIMOGENITURA: oče, Karl 6., ni imel moškega potomca + - njen sin Jožef II vlada še 10 let. Terezija se je poročila s Francem in je imela 16 otrok + - terezianizem/jožefinizem: davčne reforme: tudi plemstvo plača davke, hišne številke, štetje prebivalstva, zemljiške knjige-kata. + + sodne reforme: poenoteni zakoni, fevdalec ne sodi podložniku, ukinitev mučenja, čarovniških procesij, fevdalnih sodstev + + skuša ukiniti cehe, poenotenje mer in uteži, PROMET: poštne kočije + + vojaške: nepriljubljene, vojaška obveznost med 17. in 40. letom, veliko ljudi se izmuzne (bogati, duhovniki, kmetje) + + robotniški patent: tlaka max. 3 dni na teden, NEVOLNIŠKI/PODLOŽNIŠKI: odprava osebne odvisnosti + + šolske: splošna šolska uredba: obvezno šolanje 6-12 let M&Ž, šole: normalke, glavne šole, trivialke + + zdravstvene: babiške šole in medicinsko-kirurške + + cerkvene: vsaka cerkev max. 1h hoda, tolerančni paket 1781: svoboda vseh veroizpovedi, Jožef II. zapre veliko samostanov + +# TODO: franki -- cgit v1.2.3 From a933e6ac679fdf7596b5ee01a77676507bcc5f3f Mon Sep 17 00:00:00 2001 From: sijanec Date: Tue, 22 Dec 2020 20:51:18 +0100 Subject: zgo ocena 1: nizozemska osvoboditev --- zgo/ocena/1/dokument.md | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/zgo/ocena/1/dokument.md b/zgo/ocena/1/dokument.md index fa4c5d8..02f19ff 100644 --- a/zgo/ocena/1/dokument.md +++ b/zgo/ocena/1/dokument.md @@ -183,4 +183,12 @@ Prvo spraševanje zgodovine. + zdravstvene: babiške šole in medicinsko-kirurške + cerkvene: vsaka cerkev max. 1h hoda, tolerančni paket 1781: svoboda vseh veroizpovedi, Jožef II. zapre veliko samostanov +# nizozemska osvobodilna vojna + +* nizozemska je del španskega imperija (1. absolutna monarhija), Filip II vlada in od 17 provinc dobiva španija davke +* katoliški španci preganjajo nizozemske protestante, 1566 se nizozemci povežejo, verske zahteve postavijo kralju + - filip pošlje vojsko, vodi jo Alba, verska vojna za avtonomijo, osvobodilna vojna traja do 1648 + - [J] province se 1578 pogodijo s kraljem, [S] se povežejo v UTRECHTSKO ZVEZO, potrjeno ZDR. KRALJEVINO NIZOZ. - 1. meščan. revol. +* državni upravitelj: Viljem Oranski, Amsterdam: pomorska sila, ni fevdalizma, svob. vera, liberalni, oblast: generalni stanovi + # TODO: franki -- cgit v1.2.3 From 3e611d4de5772b04ae11eba81ebf2c9e8f0fafc1 Mon Sep 17 00:00:00 2001 From: sijanec Date: Tue, 22 Dec 2020 21:19:58 +0100 Subject: =?UTF-8?q?angle=C5=A1ka=20zgodovina?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- zgo/ocena/1/dokument.md | 20 +++++++++++++++++++- 1 file changed, 19 insertions(+), 1 deletion(-) diff --git a/zgo/ocena/1/dokument.md b/zgo/ocena/1/dokument.md index 02f19ff..1618f39 100644 --- a/zgo/ocena/1/dokument.md +++ b/zgo/ocena/1/dokument.md @@ -191,4 +191,22 @@ Prvo spraševanje zgodovine. - [J] province se 1578 pogodijo s kraljem, [S] se povežejo v UTRECHTSKO ZVEZO, potrjeno ZDR. KRALJEVINO NIZOZ. - 1. meščan. revol. * državni upravitelj: Viljem Oranski, Amsterdam: pomorska sila, ni fevdalizma, svob. vera, liberalni, oblast: generalni stanovi -# TODO: franki +# angleška zgodovina + +* normani: + - bitka pri Hastingu 1066 - Viljem Osvajalec postane angleški kralj, normani pridejo v ANG-vikingi z danske, ki so naselili [Z] FR + - pred normani so tam briti, kelti, anglosasi. trdna osrednja oblast, dobra org., kraljestvo razd. na grofije-normanski vazali +* MAGNA CARTA LIBERTATUM 1215: IVAN BREZ ZEMLJE: Brat Riharda Levjesrčnega, izgubljal zemljo, vedno več davkov, nima podpore + - upor plemstva, ivan prisiljen z listino potrditi fevdalne pravice, meščanske privilegije, neodvisnost cerkve + + vladanje postane skupna stvar kralja, izvoljenih stanov, kraljevskega sveta (ob. anglški parlament), se ne razvije absolutizem + - angleški parlament: zgornji: LOROSKA ZBORNICA-višje plemstvo, spodnji: kraljeva mesta, nižje plemstvo } dom + + odloča o davkih, nadzira državne finance, potrjuje zakone, PARLAMENTARNA MONARHINA: omejena kraljeva oblast +* stoletna vojna-ang:francozi zaradi dinastičnih sporov zaradi zemlje, pomemben mejnik, 14.-15. st. + - IVANA ORLEANSKA: kot fant 1429 reši oblegani ORLEANS, kralj razpusti vojsko, kasneje jo sežgejo + - posledice vojne: zmaga FR-centralizacija, državljanska vojna v ANG (dve roži: bela-YORK, rdeča-LANCHESTER), dinastija TUDOR 1485 +* angleška revolucija: hočejo absolutizem, zaradi MCL ne morejo, začetek: 1642-Oliver Cromwell-Lord Protector + - po cromwellovi smrti želijo obnoviti monarhijo brez prelivanja krvi, parlament-zakonodajna, kralj-izvršilna veja oblasti + - Viljem podpiše Bill of Rights: svoboda govora v parlamentu, ... + - po smrti elizabete oblast dobi Jakob I. iz škotske dinastije, Stuarti skušajo zavladati in obnoviti absolutizem + - Wiljem Oranski, zet Jakoba II.-nizozemca dobi prestol, 1688 je konec revolucije, podpis, zavladata Viljem in Mary + - Imamo vige (podreditev kralja parlamentu) in torijce (predstavniki visokega plemstva, konzervativci) -- cgit v1.2.3 From b43a09a748166cd2354f516442c2b5386b018a9e Mon Sep 17 00:00:00 2001 From: sijanec Date: Tue, 22 Dec 2020 22:08:33 +0100 Subject: zgodovina 1, kinda final --- zgo/ocena/1/dokument.md | 34 ++++++++++++++++++++++++++++++++++ 1 file changed, 34 insertions(+) diff --git a/zgo/ocena/1/dokument.md b/zgo/ocena/1/dokument.md index 1618f39..3bd0ea9 100644 --- a/zgo/ocena/1/dokument.md +++ b/zgo/ocena/1/dokument.md @@ -94,9 +94,15 @@ Prvo spraševanje zgodovine. - cerkev podredi državi-cezaropapizem, se upre vojski, uradništvu * Bizantinsko cesarstvo: helenistična kultura, vpliv krščanske vere, rimskega prava * kodeks justinjanus: manjši vpliv očeta na otroke, preganj. krivovercev, bolj svobodni sužnji, prepoved ločitve (ironic), trg z [Z] +* justinijan je bil despot, vladal je samovoljno +* HERAKELJ: tematska ureditev, vojaško upravna okrožja, delitev na pokrajine, zgodnja oblika fevdalizma, zemlja vojakom za delo +* po 7. stoletju vedno bolj helenistični videz # frankovska država +* konec 5. stoletja, ozemlje [Z] rimskega cesarstva, kralj Klodvik (480-511) iz Merovingov združi frenkovstva plemena, razširi obl. +* država: kraljeva last, deljena med sinove, to oslabi moč države, zemljo za nagrado +* majordomo: upravitelj kraljevih posesti in dvora * senior zemljo da vazalu, medsebojne dolžnosti (fevdni odnosi) ali pa odvzem zemlje. vrhovni senior je vladar. * tudi vazal je fevdalec, podložnik pa ni. nižje plemstvo nima fevdov/so premajhni. * prej so bili začasni, v času karolingov postanejo fevdi dedni. @@ -107,6 +113,25 @@ Prvo spraševanje zgodovine. * tlaka: izmerjena/določena (napovedana) ali neizmerjena/nedoločena (dodatna tlaka). podložnike obveznosti so v Z. K./urbarjih * dajatve navadnim in cerkvenim fevdalcem: velika pravda-žito/vino, mala: izdelki/storitve, dajatve za javno upravo, 1/10 cerkvi +# karolinška država + +* Karel Martel (732) (martel-kladivo) premaga Arabce pri Poitiersu, prepreči širjenje arabske države proti iberskem polotoku-8.st. + - cerkvi odvzame posest - vzpon Karolingov + - bil je majordom Marovinškemu kralju, Merovingi so še vedno na oblasti +* Pipin Mali: priskoči na pomoč papežu proti langobardom: pipnova darovnica, 751 odstavi Merovinškega kralja=>postane kralj Frankov + - v skladu s frankovsko tradicijo razdeli monarhijo med svoja sinova Karlmana in Karla Velikega +* 771 po bratovi smrti edini frankovski kralj Karel Veliki (768-814 vlada) + - razširi državo na vzhod (Langobardi, Bavarci, Obri/Avari), širi krščanstvo, 800 papež okrona za rimskega cesarja, + spor z Bizantinci, 812: sporazum v Aachnu-prestolnica, tam usrvari dvorno akademijo, Langobard Pavel Diakon, Anglosas Alguin + + dvorna akademija: gramatika, dialektika, retorika, glasba, geometrija, aritmetika, astronomija v latinščini, namen=slavi boga + + slabo izobraženi učitelji, ni efektivna šola, tako kot antične, kardinska renesansa=kulturna dejavnost v času Karla Velikega + + karolinška minuskula, pisarske dejavnosti: prepisovanje klasične kniževnosti, zgodovinopisje, germanske šege, pesnitve, navade +* delitev države: grofije/marke(mejne grofije) (200), meje grofij se spreminjajo +* razpad: lLudvig Pobožni (814-840), sin Karla Velikega, ni uspel ohraniti močisvojega očeta + - tri leta po smrti, 843 si njegovi trije sinovi v Verdunski pogodbi državo razdelijo: karel plešasti [Z], lotar I., Ludvig Nem[V] + - po Lotarjevi smrti si sredinski del razdelita ostala, ostane [V] in [Z] Frankovska država, 10.st.: [Z]=>Francija, [V]=>RN cesar. +* rekonkvista, španci so osvobodajali Iberski polotok od arabcev, med 8. in 14. stoletjem + # vzpon papeštva in nastanek cerkvene države * območje dan. IT, cerkvena organizacija sledi upravni org., patriarhat-škof/patriarh: Rim,Antiohija,Aleksandrija,Carigrad,Jeruzalem @@ -210,3 +235,12 @@ Prvo spraševanje zgodovine. - po smrti elizabete oblast dobi Jakob I. iz škotske dinastije, Stuarti skušajo zavladati in obnoviti absolutizem - Wiljem Oranski, zet Jakoba II.-nizozemca dobi prestol, 1688 je konec revolucije, podpis, zavladata Viljem in Mary - Imamo vige (podreditev kralja parlamentu) in torijce (predstavniki visokega plemstva, konzervativci) + +# etnične, družebne in gospodarske spremembe do srednjega veka do konca 18. stoletja + +* zemlja: vir preživetja in bogastva, fevdalizem: prevladujoč družbeni sistem +* stanovska družba: tisti, ki vladajo +* zemljiško gospostvo: fevd + - razviti fevdalizem: dominikalna/rustikalna, srenjska zemlja/deljena, obrtne delavnice, hube, urbarji, patrimonialna sodišča, + avtokratična/samozadostna enota + - obveznosti in dajatve: tlaka, velika&mala pravda, desetina, primščina, krpščina, priselnina -- cgit v1.2.3 From 2f735d1e8508b91067b333578ed343db1640b37e Mon Sep 17 00:00:00 2001 From: sijanec Date: Wed, 23 Dec 2020 09:05:43 +0100 Subject: dodan list z arabci --- zgo/ocena/1/dokument.md | 22 +++++++++++++++++----- 1 file changed, 17 insertions(+), 5 deletions(-) diff --git a/zgo/ocena/1/dokument.md b/zgo/ocena/1/dokument.md index 3bd0ea9..b6c59ab 100644 --- a/zgo/ocena/1/dokument.md +++ b/zgo/ocena/1/dokument.md @@ -12,7 +12,7 @@ Prvo spraševanje zgodovine. - 284-305: Dioklecijan: za 200 let vzpostavi mir - vojaške, finančne, upravne reforme; razdelitev države - tetrarhija: dva vladarja, dva namestnika, dominat: ni več senata, vladal je sam, 301 je pregnal kristjane. ga ne ubijejo. 305: rim oslabi, Dioklecijan odstopi. Dioklecijan je bil sin sužnja. - - 307-337: Konstantin: nadaljne reforme, prenese prestolnico v Konstantinopelj/Car./Ist., Milanski edikt: ne preganja več kristja. + - 307-337: Konstantin: nadaljne reforme, prenese prestolnico v Konstantinopelj/Car./Ist., Milanski edikt: ne več kristja. 313 - 379-395: Teodozij: Uspešen vojskovodja, cesar [V] rima, v [Z] tetrarhije in hitre menjave, zadnjič združi Rimski imperij + po smrti 395 razpade Rim, bitka pri Frigidu: Teodozij proti Evgeniju (pogan) - zmaga krščanstva na naših tleh. * 395 meja Rima: Beograd-Kotor-zaliv velike Sirte v [S] afriki. @@ -74,6 +74,7 @@ Prvo spraševanje zgodovine. * skupine: [V]: rusi, belorusi, ukrajinci; [J]: srbi, črnogorci, makedonci, hrvati; [Z]: poljaki, čehi, slovaki, lužiški srbi * mi delno iz [S] in panon. niž. poselimo [V] Alpe. spadamo pod južne slovane, glede na smer preseljevanja. * 6. st.: o nas in o veri piše bizantinski zgodovinar Prokopij. časimo reke, vile, divje plese, bodočnost, pojedine, petje +* so pogani, imajo obrede, zažig hiš * tujci hvalijo slovansko gostoljubnost. mel smo tut kul žene pa to... i guess... ### Avari ali Obri @@ -101,7 +102,7 @@ Prvo spraševanje zgodovine. # frankovska država * konec 5. stoletja, ozemlje [Z] rimskega cesarstva, kralj Klodvik (480-511) iz Merovingov združi frenkovstva plemena, razširi obl. -* država: kraljeva last, deljena med sinove, to oslabi moč države, zemljo za nagrado +* država: kraljeva last, deljena med 2 sinova, to oslabi moč države, zemljo za nagrado * majordomo: upravitelj kraljevih posesti in dvora * senior zemljo da vazalu, medsebojne dolžnosti (fevdni odnosi) ali pa odvzem zemlje. vrhovni senior je vladar. * tudi vazal je fevdalec, podložnik pa ni. nižje plemstvo nima fevdov/so premajhni. @@ -127,10 +128,12 @@ Prvo spraševanje zgodovine. + slabo izobraženi učitelji, ni efektivna šola, tako kot antične, kardinska renesansa=kulturna dejavnost v času Karla Velikega + karolinška minuskula, pisarske dejavnosti: prepisovanje klasične kniževnosti, zgodovinopisje, germanske šege, pesnitve, navade * delitev države: grofije/marke(mejne grofije) (200), meje grofij se spreminjajo -* razpad: lLudvig Pobožni (814-840), sin Karla Velikega, ni uspel ohraniti močisvojega očeta +* karl matel -> pipin mali -> karl veliki -> ludvig pobožni -> karl plešasti in ludvig nemški +* razpad: Ludvig Pobožni (814-840), sin Karla Velikega, ni uspel ohraniti močisvojega očeta - tri leta po smrti, 843 si njegovi trije sinovi v Verdunski pogodbi državo razdelijo: karel plešasti [Z], lotar I., Ludvig Nem[V] - po Lotarjevi smrti si sredinski del razdelita ostala, ostane [V] in [Z] Frankovska država, 10.st.: [Z]=>Francija, [V]=>RN cesar. * rekonkvista, španci so osvobodajali Iberski polotok od arabcev, med 8. in 14. stoletjem +* karolinška renesansa: združitev antične krščanske kulture z germansko, kulturni razcvet # vzpon papeštva in nastanek cerkvene države @@ -156,6 +159,7 @@ Prvo spraševanje zgodovine. + gre na pot odpuščanja v Kanoso (IT), papež mu po treh dneh čakanja zunaj na mrazu oprosti in prekliče izobčenje. - 1122: Wormski konkordat - pogodba cerkev:država, zmagajo klinijske zahteve (Cluny-mesto s samostanom), zmaga menihov in papeštva + trajna odprava laične investiture, uvedba celibata, prepoved simonije/prodaje cerkvenih služb, latinščina=edini jezik bogoslu. +* INTEREGNUM/brezvladje: 1254-1273, 1273 veliki knezi izvolijo Rudolfa Habsburškega, zmaga nad Otokarjem II. premišljenim, =>mir ## križarske vojne (3. problem) @@ -184,7 +188,7 @@ Prvo spraševanje zgodovine. - skupnost vodijo TRIBUNI: izbrani predstavniki teritorialno-vojaške aristokracije, nad njimi bizantinski vojvoda DUX/DOŽ + da se prepreči korupcijo, ga ljudstvo voli. z razvojem plemstva se krepi povezava v VELIKI SVET * ostala mesta: Genova, Pisa, Amalfi - močne pomorske sile; firence - tekstil -* meceni: financirajo učence, humanizem; diplomati, najemniške vojske +* meceni: financirajo učence, humanizem; diplomati: v tujini predstavljajo državo, kontalieri: najemniška vojska, najemniške vojske # absolutizem @@ -192,7 +196,7 @@ Prvo spraševanje zgodovine. * oporo mu nudi uradništvo, davki, vojska, cerkev, centralizirana uprava; država ima velike finančne potrebe. * prva absolutna monarhija: v španiji v 16. st. => močna država * 10. st.: Kapetingi: šibka osrednja oblast, 13.-14. st.: vojna med anglijo in francijo (dinastija Valois) - - Hugenotske vojne v protireformacije in Dinastija Bourbonov - Ludvik XIV. / sončni kralj + - Hugenotske vojne v protireformacije in Dinastija Bourbonov - Ludvik XIV. / sončni kraj - absolutizem vpeljeta kardinal Richelien in Mazarin. v klasičnem absolutizmu ni reform * razsvetljeni absolutizem omogoča reforme in je kritičen do absolutizma, zadnji poskus ohranitve fevdalizma z reformami: - FIZIOKRATIZEM: zemlja je sveta in ima edina novo vrednost, poudarek na kmetijstvu, z reformami se pomaga kmetom in 3. stanu. @@ -208,6 +212,13 @@ Prvo spraševanje zgodovine. + zdravstvene: babiške šole in medicinsko-kirurške + cerkvene: vsaka cerkev max. 1h hoda, tolerančni paket 1781: svoboda vseh veroizpovedi, Jožef II. zapre veliko samostanov +# arabci in španija + +* kordobski kulitat, arabci zavzamejo skoraj cel Pirenejski polotok po zmagi nad Vizigoti leta 771, REKONKVISTA +* križarske vojne; stanovska monarhija - srednjeveški stanovski parlament +* leta 1492 španski kralj Ferdinand Argonski in Izabela Kastiljska, ki združita španske državice +* GRANADA: zadnja trdnjava arabcev, preden jih arabci ven izženejo + # nizozemska osvobodilna vojna * nizozemska je del španskega imperija (1. absolutna monarhija), Filip II vlada in od 17 provinc dobiva španija davke @@ -229,6 +240,7 @@ Prvo spraševanje zgodovine. * stoletna vojna-ang:francozi zaradi dinastičnih sporov zaradi zemlje, pomemben mejnik, 14.-15. st. - IVANA ORLEANSKA: kot fant 1429 reši oblegani ORLEANS, kralj razpusti vojsko, kasneje jo sežgejo - posledice vojne: zmaga FR-centralizacija, državljanska vojna v ANG (dve roži: bela-YORK, rdeča-LANCHESTER), dinastija TUDOR 1485 + - Henrik 8. loči angleško od katoliške, po njegovi smrti: Edcard VI., Marija I. katoliška, Elizabeta I. * angleška revolucija: hočejo absolutizem, zaradi MCL ne morejo, začetek: 1642-Oliver Cromwell-Lord Protector - po cromwellovi smrti želijo obnoviti monarhijo brez prelivanja krvi, parlament-zakonodajna, kralj-izvršilna veja oblasti - Viljem podpiše Bill of Rights: svoboda govora v parlamentu, ... -- cgit v1.2.3