author: Anton Luka Šijanec <anton@sijanec.eu> 2022-02-02 22:39:19 +0100
committer: Anton Luka Šijanec <anton@sijanec.eu> 2022-02-02 22:39:19 +0100
commit: 3c3c3a6b1ab5a98ef4f400d5aa615ddabf3b94c5 (patch)
tree: 3e7821a6bfca04de0ecf851a41ae00e3b7caa648
parent: dnmat (diff)
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16 files changed, 299 insertions, 8 deletions
diff --git a/ang/regijsko/moji_odgovori.js b/ang/regijsko/moji_odgovori.js
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"."}[enumerate="(I."]&gt;li:before{content:"("counter(list,upper-roman) "."}[enumerate="(1."]&gt;li:before{content:"("counter(list,decimal) "."}@media (max-width:639px){.sheet{padding:16px 0}.problem{border-radius:0}}@media print{body{height:auto;background-color:#fff;overflow:visible}.wrapper{display:block;height:auto}.header{margin:0 0 16px;height:auto;color:#000;background-color:#fff;box-shadow:none}.header-countdown{display:none}.header-title{padding:0;line-height:normal}.sheet{flex:none;padding:0}.problem{border:1px solid #ccc;box-shadow:none;page-break-inside:avoid}.submit-btn{display:none}}@keyframes loading{0%{left:0;width:0}50%{left:0;width:30%}70%{width:70%}80%{left:50%}95%{left:120%}100%{left:100%}}@-webkit-keyframes loading{0%{left:0;width:0}50%{left:0;width:30%}70%{width:70%}80%{left:50%}95%{left:120%}100%{left:100%}}</style><title>Regijsko tekmovanje - A1, A2</title></head><body><div class="wrapper"><div class="header"><div class="header-title">Regijsko tekmovanje - A1, A2</div><div time="3599939.200000003" next="3399469.3999999985" class="header-countdown"><span>Preostali čas</span><div>7:05</div></div></div><div class="sheet"><div class="problem"><p>Draga dijakinja, dragi dijak,</p><p>preden začnete reševati naloge, pozorno preberite vsa navodila in prosite nadzorne profesorje za pojasnilo, če česa ne razumete. Kasneje, med spletnim reševanjem nalog, vprašanja niso dovoljena.</p><p>Za reševanje nalog imate do 60 minut časa. Ko se bo bližal konec reševanja nalog, se bo polje z uro obarvalo oranžno, tik pred koncem pa še rdeče.</p><p>Želimo vam veliko uspeha.</p><p>IATEFL Slovenia in državna tekmovalna komisija</p></div><div class="problem num"><div class="problem-statement"><h2><b>Task one</b></h2><p><b>Read the article and then decide if the statements in the table below are TRUE, FALSE or NOT GIVEN. There is only one possible answer for each statement.</b></p><p><b>SPIN IT</b></p><p>The <b>whirling dervish</b> and the <b>B-boy</b>, seven centuries and 8,ooo kilometres apart, are inextricably linked by a joy in movement and the continuous search for perfection</p><p>At a block party in the Bronx in the mid-1970s, and a bustling Turkish market in the mid-1270s, the same thing happened. The rhythm of the streets – a hip-hop sound system, the hammering of gold-beaters working their precious metal – was picked up like a radio signal and used to develop a new way of movement.</p><p>The New York hip-hop kids started the B-Boy movement with their spins and breakdances. Breaking, as the dancers themselves call it, is a pillar of hip-hop culture that originated in New York in the 1970s and is commonly referred to as a subculture of resistance. Two dimensions are intertwined in breakdance: the significance of utopian aspirations and the role of the body in subjective transformation. The participants enact utopian values in breaking, for instance by affirming the value of street life and people from the streets. Furthermore, breaking leads to subjective transformation among its young practitioners and the body plays a central role in this change of subject position. It is interesting that girls use breaking to rebel against dominant images of ideal womanhood, resulting in changes in gendered subjectivity. Hence, from disempowered, marginalised young people, breakers turn into determined agents with physical strength and emotional resilience. The dedication and discipline required to become a breaker demonstrates that these youth hold socially valued qualities with which they aim to claim a dignified place in society.</p><p>Seven hundred years before them, Rumi, a poet and a teacher of Sufi, a mystic branch of Islam, heard the gold-beaters bang, along with the religious chants they used to keep time, and began to whirl around the marketplace in the city of Konya. His was a more overtly religious experience, but, in those moments when the ground was broken for breakdancing and the sema, the dance made famous by the whirling dervishes, something spiritually uplifting occured.</p><p>Upon his death in 1273, Rumi’s followers founded the Mevlevi, a Sufi order, in his honour. Sufi fraternities were first organised as an established leadership in which a member followed a prescribed discipline in service to a sheikh or master in order to establish rapport with him. A member of such a fraternity is referred to as a dervish. Dervish orders were at one time much larger in size than they are today, as the government has taken control over most Dervish monasteries. In 1925, Turkey ordered the dissolution of Sufi fraternities by decree, but the Mevlevi was preserved among small villages throughout the Middle East. In 1954, the Turkish government granted the Mevlevi order special permission to perform ritual whirling practises for tourists during two weeks each year.</p><p>''It's important to see the common point in different cultures,'' says Murat Demirhan, a Turkish B-Boy known as Joker. ''B-Boys have a master-apprentice system. So do the Mevlevis. Both are communities where newcomers respect experience, and the community itself. In my crew it was like that.''</p><p>Joker hosted a Red Bull BC One cypher at the Sirkeci railway terminal in Istanbul, Turkey's national qualifying event ahead of the world finals of the B-Boy tournament in Seoul, South Korea in November. This brought together French B-Boy Mounir Biba, the reigning world champion, and Ceyhun Varisli of the Mevlevi order. After hundreds of years in parallel, a whirling dervish and a B-Boy performed on the same stage for the first time.</p><p>Adapted from <i>The Red Bulletin, June 2013</i></p><p><b>Now read the statements and tick the correct column: TRUE, FALSE or NOT GIVEN. An example (0) has been done for you.</b></p><p><b>Example 0:</b> Turkish markets are a busy, crowded place. <b>TRUE</b></p></div><table class="problem-grid"><tr><th /><td>TRUE</td><td>FALSE</td><td>NOT GIVEN</td></tr><tr><td>1. Breakdance is a form of resistance to hip hop.</td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td></tr><tr><td>2. The breakdancer's body movement serves as a personal response to outside circumstances.</td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td></tr><tr><td>3. Committed breakers increase their ability to cope with stressful situations and crises.</td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td></tr><tr><td>4. Rumi was a great mystic and poet in the Persian language.</td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td></tr><tr><td>5. The religious order was never outlawed.</td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td></tr><tr><td>6. Today's dervish whirling is a biennial fortnight event for tourists.</td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td></tr><tr><td>7. Both groups share a similar system of passing the knowledge to the new generations.</td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td></tr><tr><td>8. The event in the largest city in Turkey took place subsequent to the world finals.</td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td><td class="check"><input type="checkbox" /><div /></td></tr></table></div><div class="problem num"><div class="problem-fill"><h2>Task two</h2><p><b>Read the text and provide synonyms for the words below. Choose them from the ten words in bold type in the text and write them in the text boxes provided.</b></p><p>Flying into Australia, I realized with a sigh that I had forgotten again who their prime minister is. I am forever doing this with the Australian prime minister--committing the name to memory, forgetting it (generally more or less instantly), then feeling terribly guilty. My thinking is that there ought to be one person outside Australia who knows. But then Australia is such a difficult country to keep track of. On my first visit, some years ago, I passed the time on the long flight reading a history of Australian politics in the twentieth century, wherein I <b>encountered</b> <b>(0)</b> the startling fact that in 1967 the prime minister, Harold Holt, was strolling along a beach in Victoria when he plunged into the surf and vanished. No <b>trace</b> of the poor man was ever seen again. This seemed doubly <b>astounding</b> to me--first that Australia could just lose a prime minister (I mean, come on) and second that news of this had never reached me. The fact is, of course, we pay shamefully <b>scant</b> attention to our dear cousins Down Under--not entirely without reason, of course. Australia is after all mostly empty and a long way away. Its population, just over 18 million, is small by world standards--China grows by a larger amount each year--and its place in the world economy is somewhere on the <b>periphery</b>; as an economic <b>entity</b>, it ranks about level with Illinois. Its sports are of little interest to us and the last television series it made that we watched with <b>avidity</b> was Skippy. From time to time it sends us useful things--opals, merino wool, Errol Flynn, the boomerang--but nothing we can't actually do without. Above all, Australia doesn't misbehave. It is stable and peaceful and good. It doesn't have a <b>coup</b>, recklessly overfish, arm a disagreeable <b>despot</b>, grow coca in <b>provocative</b> quantities, or throw its weight around in a <b>brash</b> and unseemly manner.</p><p>Adapted from: Down Under by Bill Bryson.</p><p><b>Now write the synonyms in the text boxes provided. An example (0) has been done for you.</b></p><p><b>0. CAME ACROSS - ENCOUNTERED</b></p><p><b>1. DEPOSITION</b> - <input idx="0" size="8" value="" /></p><p><b>2. NEGLIGIBLE</b> - <input idx="1" size="8" value="" /></p><p><b>3. KEENNESS</b> - <input idx="2" size="8" value="" /></p><p><b>4. OPPRESSOR</b> - <input idx="3" size="8" value="" /></p><p><b>5. VESTIGE</b> - <input idx="4" size="8" value="" /></p></div></div><div class="problem num"><div class="problem-fill"><h2>Task three</h2><p><b>TENSES</b></p><p><b>Read the following article and put the verbs in brackets into the correct form. Write your answers in the text boxes provided. Use only the FULL FORMS of the verbs given. There is an example (0) at the beginning.</b></p><p><b>The arts must do more to oppose dirty money</b></p><p>Wed 12 Dec 2018, The Guardian</p><p>Those attending the COP24 climate negotiations in Katowice, Poland, this week <b><u>ARE GREETED</u> (0 - GREET)</b> are greeted by a bizarre sight: an artistic celebration of one of the main fuels responsible for destroying the global climate. Katowice is the centre of Poland’s coal industry, and despite hosting a conference that may represent the last chance saloon when it comes to <input idx="0" size="8" value="" /> <b>(1 - TAKE)</b> meaningful action on climate change, local politicians pride themselves on the black stuff. Perhaps no different should <input idx="1" size="8" value="" /> <b>(2 - ANTICIPATE)</b> when the Intergovernmental Panel on Climate Change decided on such an inappropriate venue and to allow coal companies to sponsor the talks.</p><p>Should society <input idx="2" size="8" value="" /> <b>(3 - SURVIVE)</b> climate change with some form of civilisation intact, some of the things we are doing now will be looked at with the same moral distaste that we feel towards slavery; some legitimate parallels are supposed <input idx="3" size="8" value="" /> <b>(4 - DRAW)</b> by many earlier writers and commentators. Climate change is yet <input idx="4" size="8" value="" /> <b>(5 - HURT)</b> those <input idx="5" size="8" value="" /> <b>(6 - NOT/BEAR)</b>. Our failure to make the dramatic changes to our economy and society means we currently behave as if we own the lives of future generations and have a right to steal their lives from them. Since its beginnings, art <input idx="6" size="8" value="" /> <b>(7 - RECORD)</b> contemporary life and Katowice is no different: there is a counter-exhibition on coal by art students, drawing attention to the “dark side of coal” pushing for an end to oil sponsorship of the arts. Students also suggest publicly denouncing such resources despite “closing their own pipelines”. “Let art soar beyond what feeds it!” one wrote under his work.</p><p>The problematic of corporate sponsorship has also been challenged by many musicians. Neil Young is due to play a large concert in Hyde Park next summer. Recently he criticised the event’s sponsor, Barclays, declaring the bank a “fossil-fuel-funding entity”. <input idx="7" size="8" value="" /> <b>(8 - CONFRONT)</b>, Young said such sponsorship proved incompatible with his beliefs about the climate, and that he <input idx="8" size="8" value="" /> <b>(9 - SEEK)</b> to rectify the situation. Yesterday he claimed victory, saying the concert was now proceeding without Barclays as a sponsor. “I would rather my eco-advisers <input idx="9" size="8" value="" /> <b>(10 - WARN)</b> me about this hypocrisy earlier. To be sponsored by the same people I speak against – that’s madness!” Knowing more light should <input idx="10" size="8" value="" /> <b>(11 - SHED)</b> on this, it’s only high time others followed in his footsteps.</p><p>There’s also a strong case against continued fossil fuel sponsorship from an economic perspective. The financial sector <input idx="11" size="8" value="" /> <b>(12 - COMMENCE)</b> to divest from fossil fuels long before Neil Young made it public. Now, smart money is in renewables and the green economy. Since the Paris Agreement was adapted in November 2015, the sustainable finance agenda has been moving away rapidly.</p><p>What’s more, the EU legislation requires of all financial market players to give full information about how customers’ money is invested. Since the EU is committed to <input idx="12" size="8" value="" /> <b>(13 - HAVE/FOSSIL FUELS/PHASE OUT)</b> by 2050, any pensions for people aged under 40 that contain assets based on fossil fuels are claimed to be misdirected. Decisions <input idx="13" size="8" value="" /> <b>(14 - NOT/THROW)</b> money at fossil fuels are more and more appreciated.</p></div></div><div class="problem num"><div class="problem-fill"><h2>Task four</h2><p><b>Form new words from the words in the bracktes. Write one word in each gap. There is an example (0) at the beginning.</b></p><p><b>The Man who Betrayed Anne Frank <u>identified</u> (0 - IDENTIFICATION) after 77 years</b></p><p>Anne Frank's diary, published after her <input idx="0" size="8" value="" /> <b>(1 - DIE)</b>, is the most famous first-hand account of Jewish life during the war. The recent study suggests that a team including an ex-FBI agent said Arnold van den Bergh, an <input idx="1" size="8" value="" /> <b>(2 - FAME)</b> Jewish figure in Amsterdam, probably "gave up" the Franks to save his own family.</p><p>The team, made up of historians and other experts, spent six years toiling away <input idx="2" size="8" value="" /> <b>(3 - INVESTIGATION)</b> and, not to mention, arduously, to crack the "cold case". That included using computer algorithms to search for connections between many different people, something that would have taken humans thousands of hours.</p><p>Van den Bergh had been a member of Amsterdam's Jewish Council, a body forced to implement Nazi policy in Jewish areas. After its <input idx="3" size="8" value="" /> <b>(4 - BAND)</b> in 1943, its members were dispatched to concentration camps. But the team found that van den Bergh was not sent to a camp, and was instead living in Amsterdam as normal at the time. There was also a suggestion that a member of the Jewish Council had been feeding the Nazis <input idx="4" size="8" value="" /> <b>(5 - DISPENSE)</b> information.</p><p>"When van den Bergh lost all his series of protections exempting him from having to go to the camps, he had to provide an <input idx="5" size="8" value="" /> <b>(6 - VALUE)</b> piece of info to the Nazis that he's had contact with to let him and his wife at that time stay safe," former FBI agent Vince Pankoke told CBS 60 Minutes.</p><p>The team said it had struggled with a series of <input idx="6" size="8" value="" /> <b>(7 - REVEAL)</b> one being that another Jewish person was probably behind the <input idx="7" size="8" value="" /> <b>(8 - BETRAY)</b>. But it also found lots of <input idx="8" size="8" value="" /> <b>(9 - EVIDENT)</b> suggesting Otto Frank, Anne's father, may himself have known that and kept it secret.</p><p>In the files of a previous investigator, they found a copy of an anonymous note sent to Otto Frank <input idx="9" size="8" value="" /> <b>(10 - IDENTITY)</b> Arnold van den Bergh as his betrayer. Mr Pankoke told 60 Minutes that anti-Semitism may have been the reason it was never made public. "Perhaps he just felt that if I bring this up again… it'll only stoke the fires further," he said.</p><p>"But we have to keep in mind that the fact that [van den Bergh] was Jewish and that meant it was not <input idx="10" size="8" value="" /> <b>(11 - COWARD)</b> but the untenable position in which he was put by the Nazis that made him do something to save his life. "Dutch newspaper de Volkskrant reports that van den Bergh died in 1950.</p><p>In a statement, the Anne Frank House museum said it was "impressed" with the investigation team's work. Its executive director, Ronald Leopold, says research value is <input idx="11" size="8" value="" /> <b>(12 - EXAMPLE)</b> by the new research that had "generated important new information and a fascinating hypothesis that merits <input idx="12" size="8" value="" /> <b>(13 - FAR)</b> research".</p><p>The museum said it was only <input idx="13" size="8" value="" /> <b>(14 - DIRECT)</b> involved in the investigation but had shared its archives and museum with the team.</p></div></div><div class="problem num"><div class="problem-fill"><h1>Task five</h1><p><b>Read the sentences and decide which of the four answers from the drop-down menu best fits each gap. Select one possible answer.</b> <b>An example (0) has been done for you.</b></p><p><b>0.</b> »It's hot in here.« - »__________ I open the window?«</p><p>a) Will <b>b) Shall</b> c) Do d) Would</p><p>1. When Mary woke up, the sun <select idx="0"><option /><option>a) shun</option><option>b) shone</option><option>c) was shinning</option><option>d) shined</option></select> .</p><p>2. By the time I go out tonight I <select idx="1"><option /><option>a) will have prepared</option><option>b) will prepare</option><option>c) would prepare</option><option>d) prepared</option></select> my presentation on natural disasters</p><p>3. <select idx="2"><option /><option>a) Had been handing</option><option>b) Having handed</option><option>c) Had given</option><option>d) Giving</option></select> in my seminar paper, I realised that I had forgotten to put my name on it.</p><p>4. Ms Bettencourt Meyers <select idx="3"><option /><option>a) is said</option><option>b) is said that</option><option>c) is said that she is</option><option>d) is said to be</option></select> the richest woman in the world.</p><p>5. At first, many sushi restaurants weren’t at all successful in the Balkans, but they eventually <select idx="4"><option /><option>a) picked out</option><option>b) caught on</option><option>c) logged on</option><option>d) tapped on</option></select> in the capital cities.</p><p>6. I hate this cold and foggy weather! <select idx="5"><option /><option>a) I wish I had been</option><option>b) Only if I were</option><option>c) If only I had been</option><option>d) I wish I were</option></select> on a tropical island right now.</p><p>7. How did you find out about the secret surprise for Mum and Dad? Did Grandma <select idx="6"><option /><option>a) shout the odds</option><option>b) make it rain</option><option>c) kicked the bucket</option><option>d) spill the beans</option></select> again?</p><p>8. Roger's car has only four seats but it can carry six people in <select idx="7"><option /><option>a) a nutshell</option><option>b) a rut</option><option>c) a pinch</option><option>d) full swing</option></select>.</p><p>9. Everyone who forgot to hand in their assignments on time found themselves <select idx="8"><option /><option>a) in Slovene</option><option>b) in Dutch</option><option>c) in Scottish</option><option>d) in French</option></select>.</p><p>10. This kind of chance comes once in a <select idx="9"><option /><option>a) pink</option><option>b) red</option><option>c) silver</option><option>d) blue</option></select> moon. You should really appreciate it.</p></div></div><div class="problem num"><div class="problem-fill"><h2>Task six</h2><p><b>Read the text and fill each gap with only ONE suitable word. An example (0) has been done for you.</b></p><p><b>Every Student’s Nightmare: A Teacher with the “You-Just-Have-to-Read-This-Book!”</b></p><p>When faced <u><b>with</b></u> <b>(0)</b> contemporary novels, students would often <input idx="0" size="8" value="" /> <b>(1)</b> an eyebrow and feel <input idx="1" size="8" value="" /> <b>(2)</b> out of the usual storyline or predictability. This may displease some language teachers, but we need to <input idx="2" size="8" value="" /> <b>(3)</b> in mind that any <input idx="3" size="8" value="" /> <b>(4)</b> person who has had their predictions and set patterns (even such of reading) crushed is not <input idx="4" size="8" value="" /> <b>(5)</b> take it lightly. Needless to say, contemporary novels are, frankly, no light <input idx="5" size="8" value="" /> <b>(6)</b>.</p><p>In fact, we need to prepare students for the challenging <input idx="6" size="8" value="" /> <b>(7)</b> any way we can and allow them to be displeased about the work <input idx="7" size="8" value="" /> <b>(8)</b> fond (and biased?) we may be towards it. There’s nothing more terrible than a teacher who wants to <input idx="8" size="8" value="" /> <b>(9)</b> their own affection for a piece of literature reflected in student’s mouths. Help them <input idx="9" size="8" value="" /> <b>(10)</b> appreciation for the intricate mastery of writing and in <input idx="10" size="8" value="" /> <b>(11)</b> such a way they might risk <input idx="11" size="8" value="" /> <b>(12)</b> other similar works a go.</p><p>How, you ask? Have them immersed <input idx="12" size="8" value="" /> <b>(13)</b> the time and setting of <input idx="13" size="8" value="" /> <b>(14)</b> the author and the storyline. Don’t be afraid of provocative questions, or perhaps act passages out in front of the class. Sometimes a bit of live action is enough to connect the dots <input idx="14" size="8" value="" /> <b>(15)</b> previously missing.</p></div></div><div class="problem num"><div class="problem-statement"><h1>Task seven</h1><p><b>Complete the sentences based on Mark Haddon's <i>The Curious Accident of the Dog in the Night-Time</i>: A, B or C. There is only one possible answer.</b></p></div><div class="problem-substatement">1. The main character of the novel likes</div><label class="problem-answer"><input type="checkbox" /><div />a) the colours yellow and brown.</label><label class="problem-answer"><input type="checkbox" /><div />b) lists and patterns.</label><label class="problem-answer"><input type="checkbox" /><div />c) being touched.</label><div class="problem-substatement">2. According to Christopher, a dog has the following four moods:</div><label class="problem-answer"><input type="checkbox" /><div />a) happy, agitated, aggressive, pensive.</label><label class="problem-answer"><input type="checkbox" /><div />b) happy, anxious, playful, aggressive.</label><label class="problem-answer"><input type="checkbox" /><div />c) happy, sad, cross, concentrating.</label><div class="problem-substatement">3. When Father is able to see Christopher at the police station,</div><label class="problem-answer"><input type="checkbox" /><div />a) Christopher gives him a hug.</label><label class="problem-answer"><input type="checkbox" /><div />b) he appears to be angry with his son.</label><label class="problem-answer"><input type="checkbox" /><div />c) they don’t hug but make a special gesture with their fingers.</label><div class="problem-substatement">4. In Christopher’s order of things seeing four yellow cars in a row means</div><label class="problem-answer"><input type="checkbox" /><div />a) a black day.</label><label class="problem-answer"><input type="checkbox" /><div />b) a good day.</label><label class="problem-answer"><input type="checkbox" /><div />c) a super good day.</label><div class="problem-substatement">5. When Christopher starts doing his detective work, he first speaks to</div><label class="problem-answer"><input type="checkbox" /><div />a) Mr. Wise’s mother.</label><label class="problem-answer"><input type="checkbox" /><div />b) Mrs. Shears.</label><label class="problem-answer"><input type="checkbox" /><div />c) old lady Mrs. Alexander.</label><div class="problem-substatement">6. Christopher presumes that the culprit for Wellington’s death is</div><label class="problem-answer"><input type="checkbox" /><div />a) father.</label><label class="problem-answer"><input type="checkbox" /><div />b) Mr. Shears.</label><label class="problem-answer"><input type="checkbox" /><div />c) one of the drug addicts living next door.</label><div class="problem-substatement">7. Several people tell Christopher to</div><label class="problem-answer"><input type="checkbox" /><div />a) keep up his detective work.</label><label class="problem-answer"><input type="checkbox" /><div />b) stay out of other people’s business.</label><label class="problem-answer"><input type="checkbox" /><div />c) ask Mrs. Alexander lots of questions about Mr. Shears.</label><div class="problem-substatement">8. Where does Christopher find his missing manuscript?</div><label class="problem-answer"><input type="checkbox" /><div />a) In a shirt box in the wardrobe in Father’s bedroom.</label><label class="problem-answer"><input type="checkbox" /><div />b) In a cupboard in their living room.</label><label class="problem-answer"><input type="checkbox" /><div />c) In a cupboard in his bedroom.</label><div class="problem-substatement">9. After finding out the truth about his parents,</div><label class="problem-answer"><input type="checkbox" /><div />a) Christopher does not want to live with his father anymore.</label><label class="problem-answer"><input type="checkbox" /><div />b) Christopher still trusts his father and is happy to live under the same roof with him.</label><label class="problem-answer"><input type="checkbox" /><div />c) Christopher runs away from home immediately.</label><div class="problem-substatement">10. When Christopher turns up at Judy and Roger’s London apartment,</div><label class="problem-answer"><input type="checkbox" /><div />a) they have a shouting match.</label><label class="problem-answer"><input type="checkbox" /><div />b) Judy is not at home until very late at night.</label><label class="problem-answer"><input type="checkbox" /><div />c) Roger happily invites him to stay with them as long as necessary.</label><div class="problem-substatement">11. Christopher expressed the need to return to Swindon</div><label class="problem-answer"><input type="checkbox" /><div />a) because he wanted to go back to school and hang out with his friends.</label><label class="problem-answer"><input type="checkbox" /><div />b) because he needed to hand in a home assignment to Siobhan.</label><label class="problem-answer"><input type="checkbox" /><div />c) because he was taking an important exam very soon.</label></div><button class="submit-btn success">Shranjeno</button><div class="sheet-footer success">Vaše rešitve so bile zabeležene (31. 1. 2022 ob 15:51:26).
+Ponovna oddaja je možna do izteka predvidenega časa reševanja.
+Zadnja oddaja bo upoštevana.</div></div></div></body></html>
+\ No newline at end of file
diff --git a/fiz/vaje/2.ods b/fiz/vaje/2.ods
new file mode 100644
index 0000000..bac8716
--- /dev/null
+++ b/fiz/vaje/2.ods
diff --git a/inf/rtk/šolsko/1 b/inf/rtk/šolsko/1
new file mode 100755
index 0000000..e8daf5b
--- /dev/null
+++ b/inf/rtk/šolsko/1
diff --git a/inf/rtk/šolsko/1.c b/inf/rtk/šolsko/1.c
new file mode 100644
index 0000000..f93eb94
--- /dev/null
+++ b/inf/rtk/šolsko/1.c
@@ -0,0 +1,24 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+int main (void) {
+	char buf[1024];
+	double z = 0;
+	fgets(buf, 1024, stdin); /* prva vrstica ni potrebna */
+	fgets(buf, 1024, stdin);
+	while (!feof(stdin)) { /* gremo čez vsako vrstico */
+		int i = 0; /* indeks */
+		int m = 1; /* trenutni imenovalec */
+		do {
+			m *= 2; /* povečamo trenutni imenovalec */
+			if (buf[i] == 'S') {
+				z += 1 / (double) m; /* povečamo za trenutno velikost kosa */
+				/* fprintf(stderr, "sadi, %d, %f\n", m, z); */
+			}
+			i++;
+		} while (buf[i-1] != '\n' && buf[i-1] != 0 && buf[i-1] != '\r'); /* konec vhoda */
+		fgets(buf, 1024, stdin); /* poberemo novo vrstico */
+	}
+	printf("%d\n", (int) ceil(z)); /* izpišemo vrednost, zaokroženo navzgor */
+	return 0; /* končamo program */
+}
diff --git a/inf/rtk/šolsko/1.txt b/inf/rtk/šolsko/1.txt
new file mode 100644
index 0000000..6a912d3
--- /dev/null
+++ b/inf/rtk/šolsko/1.txt
@@ -0,0 +1,6 @@
+5 4
+SJSJ
+SSJJ
+JSJJ
+JJJJ
+JJSJ
diff --git a/inf/rtk/šolsko/2 b/inf/rtk/šolsko/2
new file mode 100755
index 0000000..58228cb
--- /dev/null
+++ b/inf/rtk/šolsko/2
diff --git a/inf/rtk/šolsko/2.c b/inf/rtk/šolsko/2.c
new file mode 100644
index 0000000..3c7f97d
--- /dev/null
+++ b/inf/rtk/šolsko/2.c
@@ -0,0 +1,30 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+int main (int argc, char ** argv) { /* vzorec je prvi argument, slovar je standardni vhod */
+	if (argc != 2) {
+		fprintf(stderr, "uporaba: %s vzorec < slovar.txt\n", argv[0] ? argv[0] : "pwnkit");
+		return 1; /* slovar so besede v cevovodu, ločene z novo vrstico tipa POSIX */
+	}
+	int l = strlen(argv[1]); /* dolžina vzorca, daljše besede avtomatsko izključimo */
+	char * buf = alloca(l+2); /* prostor za vrstico vnosa slovarja */
+#define NASLEDNJI() while (!fgets(buf, l+2, stdin) && !feof(stdin)) /* predolgi grejo takoj stran */
+	NASLEDNJI();
+	while (!feof(stdin)) { /* beremo vsako besedo slovarja */
+		for (int i = 0; 1; i++) { /* gremo čez vsak znak besede iz slovarja in znak vzorca */
+			if (buf[i] == '\n' && !argv[1][i]) { /* če je hkrati konec besede & vzorca */
+				printf("%s", buf); /* itak je nova vrstica že v buf */
+				break; /* natisnemo besedo in gremo na naslednjo besedo */
+			}
+			if (buf[i] == '\n' || (buf[i] != argv[1][i] && argv[1][i] != '*'))
+				break; /* če je konec besede in ni konec vzorca ali obratno */
+		}			/* potem ne izpišemo */
+		NASLEDNJI();
+	}
+	return 0; /* končamo program */
+}
+
+/*
+podprimer b:
+Vse besede bi shranili v delovni pomnilnik v drevesno strukturo s primerjalno funkcijo strcmp, vendar bi imeli za vsako dolžino besede svojo drevesno strukturo. Z drevesno strukturo smo olajšali kompleksnost iskanja besed, kjer je pri vzorcu na začetku veliko določenih znakov in ne zvezdic. Ko pri vzorcu pridemo do prve zvezdice, bo itak treba iskati po vsej veji v drevesu. Dodajanje dreves še od zadaj naprej bi samo povečalo spominsko zahtevnost. S ločevanjem po dolžini nizov pa smo zmanjšali kompleksnost, ko vzorec blizu začetka če vsebuje zvezdico a ni iste dolžine (takoj bo zavrnjen, če te dolžine v slovarju ni in zmanjša iskalno polje), nismo pa bistveno vplivali na spominsko zahtevnost.
+*/
diff --git a/inf/rtk/šolsko/2.txt b/inf/rtk/šolsko/2.txt
new file mode 100644
index 0000000..d35a736
--- /dev/null
+++ b/inf/rtk/šolsko/2.txt
@@ -0,0 +1,5 @@
+miza
+zima
+riba
+mirta
+prva
diff --git a/inf/rtk/šolsko/3 b/inf/rtk/šolsko/3
new file mode 100755
index 0000000..5756a55
--- /dev/null
+++ b/inf/rtk/šolsko/3
diff --git a/inf/rtk/šolsko/3.c b/inf/rtk/šolsko/3.c
new file mode 100644
index 0000000..041c723
--- /dev/null
+++ b/inf/rtk/šolsko/3.c
@@ -0,0 +1,106 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <sys/types.h>
+#include <sys/stat.h>
+#include <unistd.h>
+#include <fcntl.h>
+#include <sys/mman.h>
+
+/*
+opisno:
+
+Zmanjkalo mi je časa, zato pišem odgovor opisno, kar bi moralo biti v redu, ker bi predvsem implementacija branja podatkov porabila veliko časa pisanja programa.
+
+Torej. Preberemo podatke iz datoteke iz datoteke, kjer so vrstice ločene z novo vrstico in stolpci s presledkom v tabelo z vrednostjo.
+
+Potem v zanki gremo čez vsako vrstico in v tej zanki čez vsak stolpec - vsako polje in si izpišemo za vsak zaporeden niz polij, ki imajo vrednost, večjo od 1, celotno vrstico (glej struct linija), vrednost, začetek in konec linije in usmerjenost (glej enum usmerjenost).
+
+Potem gremo v zanki čez vsak stolpec in gledamo kot pri prejšnjem odstavku od zgoraj navzdol in si v enakem formatu, le da usmerjenost nastavimo na NAVPIČNO, zapisujemo linije z vrednostjo, večjo od 0.
+
+Pri prejšnjih dveh odstavkih tudi iščemo vrstico z linijo z največjo vrednostjo in shranimo X in Y koordinate najmanj vrednega polja (trivialno ga je najti in te koordinate zapisati v dve spremenljivki). Tukaj vrednosti enkrat odštejemo vrednost najmanj vrednega polja, saj tja postavimo žeton in se ne šteje. To odšteto vrednost pa zapišemo v spremenljivko makskalkvred, saj bomo z njo primerjali skupne vrednosi parov.
+
+Sedaj imamo vse vodoravne in navpične linije v dveh preglednih enodimenzionalnih tabelah (struct linija * linijev in struct linija * linije h). Za vsako vodoravno gremo v zanki čez seznam navpičnih in pogledamo, če se ti dve (navpična in vodoravna) liniji sekata. Sekata se, če je pozicija vodoravne linije med začetkom in koncem (vključno z začetkom in koncem). Sedaj pogledamo, ali je seštevek njunih vrednosti, potem ko mu dvakrat odštejemo vrednost polja, kjer se liniji sekata (ker tja postavimo žeton - dvakrat pa zato, kjer je to polje prisotno v obeh linijah), večji od največjega prejšnjega seštevka v spremenljivki makskalkvred, če je, zapišemo to izračunano vrednost v spremenljivko makskalkvred in X in Y koordinate polja, kjer se ti dve liniji sekata. Ena koordinata tega polja je torej pozicija navpične linije, druga pa pozicija vodoravne.
+
+Ko smo šli čez vse pare linij pa na standardni izhod izpišemo spremenljivki obeh koordinat in zaključimo program.
+
+*/
+
+struct linija {
+	int začetek;
+	int konec;
+	int pozicija;
+	int vrednost;
+};
+int main (int argc, char ** argv) {
+	if (argc != 2) {
+		fprintf(stderr, "uporaba: %s polje.txt\n", argv[0] ? argv[0] : "pwnkit");
+		return 1;
+	}
+	int fd;
+       	if ((fd = open(argv[1], O_RDONLY)) == -1) {
+		perror("open");
+		return 2;
+	}
+	struct stat statbuf;
+	if (fstat(fd, &statbuf) == -1) {
+		perror("fstat");
+		return 3;
+	}
+	char * vhod;
+	if ((vhod = mmap(NULL, statbuf.st_size, PROT_READ, MAP_SHARED, fd, 0)) == MAP_FAILED) {
+		perror("mmap");
+		return 4;
+	}
+	struct linija * linijev = NULL;
+	struct linija * linijen = NULL;
+	int linijv = 0;
+	int linijn = 0;
+	int * dolžine = NULL;
+	int ** vrstice = NULL;
+	int vrstic = 0;
+	int r = 0;
+	char * c = vhod;
+	int maksdolžina = 0;
+	do {
+		vrstice = realloc(vrstice, sizeof(*vrstice)*++vrstic);
+		dolžine = realloc(dolžine, sizeof(*dolžine)*vrstic);
+		vrstice[vrstic-1] = NULL;
+		dolžine[vrstic-1] = 0;
+		do {
+			vrstice[vrstic-1] = realloc(vrstice[vrstic-1], sizeof(*vrstice[vrstic-1])*++dolžine[vrstic-1]);
+			vrstice[vrstic-1][dolžine[vrstic-1]-1] = strtol(c, &c, 10);
+		} while (*c != '\n');
+		if (dolžine[vrstic-1] > maksdolžina)
+			maksdolžina = dolžine[vrstic-1];
+	} while (c+1 < vhod+statbuf.st_size && *c);
+	for (int i = 0; i < vrstic; i++) {
+		struct linija vrstica = {
+			.začetek = 0,
+			.konec = 0,
+			.pozicija = i,
+			.vrednost = 0
+		};
+		for (int j = 0; j < dolžine[i]; j++) {
+			if (vrstica.vrednost == 0) {
+				vrstica.začetek = j;
+			}
+			if (vrstice[i][j] == 0 && vrstica.vrednost) {
+				vrstica.konec = j;
+				linijev = realloc(linijev, sizeof(*linijev)*linijv++);
+				memcpy(linijev[linijv-1], &linija, sizeof(linija));
+				vrstica.vrednost = 0;
+			}
+			vrstica.vrednost += vrstice[i][j];
+			fprintf(stderr, "%d ", vrstice[i][j]);
+		}
+		fprintf(stderr, "\n");
+	}
+	for (int j = 0; j < maksdolžina; j++) {
+		for (int i = 0; i < vrstic; i++) {
+			//
+		}
+	}
+r:
+	munmap(vhod, statbuf.st_size);
+	return r;
+}
diff --git a/inf/rtk/šolsko/3.txt b/inf/rtk/šolsko/3.txt
new file mode 100644
index 0000000..79f4236
--- /dev/null
+++ b/inf/rtk/šolsko/3.txt
@@ -0,0 +1,4 @@
+0 0 1 2 0
+0 2 3 1 0
+0 0 2 1 2
+0 0 0 3 1
diff --git a/inf/rtk/šolsko/4.c b/inf/rtk/šolsko/4.c
new file mode 100644
index 0000000..1aa574c
--- /dev/null
+++ b/inf/rtk/šolsko/4.c
@@ -0,0 +1,27 @@
+/*
+opisna rešitev:
+
+Naredimo seznam takih elementov:
+
+enum dejanje {
+	PRIHOD,
+	ODHOD
+};
+struct dejanje {
+	int čas;
+	int dolžina;
+	enum dejanje dejanje;
+};
+
+V zanki za vsak tovornjak v ta seznam dodamo ta dejanja. Najprej dodamo dejanje s .dejanje == PRIHOD in čas prihoda, nato pa dejanje s .dejanje == ODHOD, ki vsebuje vrednost prihoda, ki ji je prištet čas postanka. V vsak element seznama dodamo tudi dolžino tovornjaka.
+
+Po velikosti uredimo glede na čas seznam dejanj s standardno funkcijo qsort(). Sortirna funkcija naj v obzir vzame tudi dejanje. Če je prvo dejanje ODHOD in drugo PRIHOD, imata pa isti čas, vrne -1 in s tem postavi ODHOD pred PRIHOD.
+
+Deklariramo številsko spremenljivko maksdolžina in jo inicializiramo na 0, prav tako naredimo spremenljivko trenutnadolžina.
+
+Gremo po urejenem seznamu v zanki in ko naletimo na element s .dejanje == PRIHOD, povečamo spremenljivko trenutnadolžina za .dolžina, ko naletimo na element s .dejanje == ODHOD, zmanjšamo spremenljivko trenutnadolžina za .dolžina. Vsakič na koncu programa v zanki preverimo, če je trenutnadolžina morebiti večja od maksdolžina, v tem primeru maksdolžina nastavimo na trenutnadolžina.
+
+Ob koncu te zanke na standardni izhod izpišemo spremenljivko maksdolžina in končamo program.
+
+*/
+
diff --git a/inf/rtk/šolsko/5.c b/inf/rtk/šolsko/5.c
new file mode 100644
index 0000000..ed777eb
--- /dev/null
+++ b/inf/rtk/šolsko/5.c
@@ -0,0 +1,22 @@
+/*
+opisna naivna rešitev: (levo pomeni z manjšim indeksom, desno pa z večjim indeksom)
+
+Naredimo seznam z elementi:
+
+struct stoplnica {
+	int višina;
+	int indeks;
+	int barva; // barva je na začetku siva - 0
+};
+
+Sedaj moramo spremeniti vsak element seznama tako, da noben element seznama ne bo imel .barva == 0.
+
+Naredimo spremenljivko maksbarva in jo inicializiramo na 0.
+
+Začnemo pri elementu 0. Najti moramo element z nastavljeno barvo (torej .barva != 0), ki ga ne vidimo.
+
+Gledamo element vedno bolj levo, dokler ne dobimo takega, ki ga ne vidimo in ni direktno poleg nas (njegov desni element ne smemo biti mi). Ko ga najdemo, uporabimo to barvo elementa kot našo barvo. Če pridemo do začetka seznama, povečamo spremenljivko maksbarva in trenutnemu elementu nastavimo .barva na maksbarva.
+
+Ko nastavimo barvo zadnjemu elementu, izpišemo spremenljivko maksbarva na standardni izhod in zaključimo program.
+
+*/
diff --git a/inf/rtk/šolsko/Makefile b/inf/rtk/šolsko/Makefile
new file mode 100644
index 0000000..1dd50ea
--- /dev/null
+++ b/inf/rtk/šolsko/Makefile
@@ -0,0 +1,15 @@
+CFLAGS += -Wextra -Wall -pedantic -g -O0 -finput-charset=UTF-8 -fanalyzer -fextended-identifiers
+LDFLAGS += -lm
+CC ?= cc
+SHELL ?= /bin/sh
+cbins := $(subst .c,,$(wildcard *.c))
+asmbins := $(subst .asm,,$(wildcard *.asm))
+default: $(cbins) $(asmbins)
+%: %.c
+	$(CC) $(CFLAGS) $< -o$@ $(LDFLAGS)
+%: %.asm
+	# za zdaj sicer še ni ničesar v zbornem jeziku, mogoče pa bo ...
+	nasm -f elf $< && ld -m elf_i386 -s -o $@ $@.o
+.PHONY: clean
+clean:
+	rm -f $(bins) $(asmbins) *.o
diff --git a/mat/trigonometrija.tex b/mat/trigonometrija.tex
index cb65720..c9cfff5 100644
--- a/mat/trigonometrija.tex
+++ b/mat/trigonometrija.tex
@@ -11,6 +11,7 @@
 \usepackage{tkz-euclide}
 \usepackage{amssymb}
 \usepackage{multicol}
+\usepackage{amsmath}
 % \sisetup{output-decimal-marker = {,}, quotient-mode=fraction, per-mode=fraction}	% frac način
 % \sisetup{output-decimal-marker = {,}, quotient-mode=fraction, per-mode=symbol}	% poševnica način
 \sisetup{output-decimal-marker = {,}, quotient-mode=fraction}				% na -1 način
@@ -35,18 +36,21 @@
 % Spisek izbranih trigonometričnih izrekov bom kot pripomoček imel na drugem testu pri matematiki v tretjem letniku.
 % \end{abstract}
 % \tableofcontents
+\section{Drugi test}
 \begin{multicols}{2}
-	\begin{tabular}{|c|c|c|c|c|}
+	\begin{tabular}{|c|c|c|c|c|c|}
 		\hline
-		$\measuredangle$	& $\sin$		& $\cos$		& $\tan$		& $\cot$		\\
+		$\measuredangle$	& Rad		& $\sin$		& $\cos$		& $\tan$		& $\cot$		\\
 		\hline
-		$\ang{30}$		& 0			& 1			& 0			& ne obstaja		\\
+		$\ang{0}$		& 0		& 0			& 1			& 0			& ne obstaja		\\
 		\hline
-		$\ang{45}$		& $\frac{1}{2}$	& $\frac{\sqrt{3}}{2}$	& $\frac{\sqrt{3}}{2}$	& $\sqrt{3}$		\\
+		$\ang{30}$		&$\frac{\pi}{6}$& $\frac{1}{2}$		& $\frac{\sqrt{3}}{2}$	& $\frac{\sqrt{3}}{2}$	& $\sqrt{3}$		\\
 		\hline
-		$\ang{60}$		& $\frac{\sqrt{3}}{2}$	& $\frac{1}{2}$		& $\sqrt{3}$		& $\frac{\sqrt{3}}{3}$	\\
+		$\ang{45}$		& $\frac{\pi}{4}$& $\frac{\sqrt{2}}{2}$	& $\frac{\sqrt{2}}{2}$	& 1			& 1			\\
 		\hline
-		$\ang{90}$		& 1			& 0			& ne obstaja		& 0			\\
+		$\ang{60}$		& $\frac{\pi}{3}$& $\frac{\sqrt{3}}{2}$	& $\frac{1}{2}$		& $\sqrt{3}$		& $\frac{\sqrt{3}}{3}$	\\
+		\hline
+		$\ang{90}$		& $\frac{\pi}{2}$& 1			& 0			& ne obstaja		& 0			\\
 		\hline
 	\end{tabular}
 	$$\sin^2\alpha+\cos^2\alpha=1$$
@@ -80,12 +84,37 @@
 	$$\sin\alpha\pm\sin\beta=2\sin\left(\frac{\alpha\pm\beta}{2}\right)\cos\left(\frac{\alpha\mp\beta}{2}\right)$$
 	$$\cos\alpha+\cos\beta=2\cos\left(\frac{\alpha+\beta}{2}\right)\cos\left(\frac{\alpha-\beta}{2}\right)$$
 	$$\cos\alpha-\cos\beta=-2\sin\left(\frac{\alpha+\beta}{2}\right)\sin\left(\frac{\alpha-\beta}{2}\right)$$
-	$$\tan\alpha+\tan\beta=\frac{\sin\left(\alpha+\beta\right)}{\cos\alpha\cos\beta}$$
+	$$\tan\alpha\pm\tan\beta=\frac{\sin\left(\alpha\pm\beta\right)}{\cos\alpha\cos\beta}$$
 	$$\sin\alpha\cos\alpha=\frac{1}{2}\sin2\alpha$$
 	$$2\cos^2\frac{\alpha}{2}=1+\cos\alpha$$
 	$$2\sin^2\frac{\alpha}{2}=1-\cos\alpha$$
 	$$\tan^2\frac{x}{2}=\frac{1-\cos\alpha}{1+\cos\alpha}$$
-	$$\cos\frac{\alpha}{2}=\pm\sqrt{\frac{1+\cos\alpha}{2}} \text{ in tako dalje}$$
+\end{multicols}
+\section{Tretji test}
+\begin{multicols}{2}
+	$$s=\frac{a+b+c}{2} \wedge S=\sqrt{s(s-a)(s-b)(s-c)}$$
+	$$S_\text{trikotnika v izseku}=\frac{r^2\sin\alpha}{2}$$
+	$$\frac{a}{\sin\alpha}=\frac{b}{\sin\beta}=\frac{c}{\sin\gamma}=2R$$
+	$$a^2=b^2+c^2-2bc\cos\alpha$$
+	$$S_\text{paralelograma}=av_a=ab\sin\alpha=\frac{ef}{2}\sin\omega$$
+	$$S_\text{romba}=av=a^2\sin\alpha=\frac{ef}{2}$$
+	$$S_\text{trapeza}=\frac{v(a+c)}{2}$$
+	$$S_\text{deltoida}=\frac{ef}{2}$$
+	$$S_\text{trikotnika}=\frac{ab\sin\gamma}{2}=\frac{av_a}{2}$$
+	$$S_\text{enakostraničnega}=\frac{a^2\sqrt{3}}{4}$$
+	$$\arcsin x+\arccos x=\frac{\pi}{2}$$
+	$$S_\text{trikotnika}=\frac{abc}{4R}=2R^2\sin\alpha\sin\beta\sin\gamma=rs\text{, kjer je } s=\frac{a+b+c}{2}$$
+	$$Diagonal_\text{pravilnega mnogokotnika}=\frac{n(n-3)}{2}$$
+	$$\alpha_\text{pravilnega mnogokotnika}=\frac{n-2}{n}\ang{180}$$
+	$$S_\text{pravilnega mnogokotnika}=\frac{n}{2}R^2\sin\frac{\ang{360}}{n}=
+		na^2\tan\frac{\alpha}{2}\frac{1}{2}=\frac{na^2}{4\tan\frac{\ang{180}}{n}}$$
+	$$\alpha_\text{ene premice}=\arctan k_p$$
+	$$\alpha_\text{med dvema premicama}=\arctan\lvert\frac{k_q-k_p}{1+k_p-k_q}\rvert$$
+	$$D_\text{arcsin}=D_\text{arccos}=[-1; 1] \wedge V_\text{arcsin}=[\ang{-90}; \ang{90}] \wedge V_\text{arccos}=[\ang{0}; \ang{180}]$$
+	$$D_\text{arctan}=D_\text{arccot}=\mathbb{R} \wedge V_\text{arctan}=(\ang{-90}; \ang{90}) \wedge V_\text{arccot}=(\ang{0}; \ang{180})$$
+	$$soda(x)=-soda(x) \wedge liha(-x)=-liha(x)$$
+	$$f(x)\neq-f(x)\nLeftrightarrow f(-x)=-f(x) \text{ in obratno}$$
+	$$f(x)=-f(x) \wedge f(-x)=-f(x) \Leftrightarrow f(x)=0$$
 \end{multicols}
 \section{Zaključek}
 \hologo{LaTeX} izvorna koda dokumenta je objavljena na \url{https://git.sijanec.eu/sijanec/sola-gimb-3}. Za izdelavo dokumenta je potreben \texttt{TeXLive 2020}.
author	Anton Luka Šijanec <anton@sijanec.eu>	2022-02-02 22:39:19 +0100
committer	Anton Luka Šijanec <anton@sijanec.eu>	2022-02-02 22:39:19 +0100
commit	3c3c3a6b1ab5a98ef4f400d5aa615ddabf3b94c5 (patch)
tree	3e7821a6bfca04de0ecf851a41ae00e3b7caa648
parent	dnmat (diff)
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