Questões - ITA 2004 | Gabarito e resoluções

(ITA - 2004 - 1a Fase) Considere a funo f: IR ,f(x) = 2 cos x + 2i sen x. Ento, x, y IR o valor do produto f(x)f(y) igual a

(ITA - 2004 - 1a Fase) Em 1879, Edwin Hall mostrou que, numa lmina metlica, os eltrons deconduo podem ser desviados por um campo magntico, tal que no regime estacionrio, hum acmulo de eltrons numa das faces da lmina, ocasionando uma diferena de potencialVH entre os pontos P e Q, mostrados na figura. Considere, agora, uma lmina de cobre deespessura L e largura d, que transporta uma corrente eltrica de intensidade i, imersa nocampo magntico uniforme B que penetra perpendicularmente a face ABCD, no mesmosentido de C para E. Assinale a alternativa CORRETA.

(ITA - 2004 - 1a Fase) First, let me tell you where Im coming from. Before I saw The Lord of the Rings: The Fellowship of the Ring, I didnt know the difference between an orc and an elf, or what Middle-earth was in the middle of. Thisreview is coming to you from a Tolkien-freezone. I went in to Peter Jacksons movie the first of a trilogy with no preconceptions. I came out, three hours later, sorry Id have to wait a year to see whathappens next in Frodo Bagginss battle against the Dark Lord, Sauron, and thinking a trip to the bookstore to pick The Two Towers might be in order. (...) This is a violent movie too violent for little ones and there are moments more Matrix than medieval. Yet it transcends cheap thrills; we root for the survival of our heroes with a depth of feeling that may come as a surprise. The movie keeps drawing you in deeper. Unlike so many overcooked action movies these days, Fellowship doesnt entertain you into a stupor. It leaves you with your wits intact, hungry for more. (fonte omitida para evitar induo na resposta) Os termos Yet e Unlike, no segundo pargrafo, significam, respectivamente,

(ITA - 2004 - 1a Fase) Considere 12 pontos distintos dispostos no plano, 5 dos quais esto numa mesma reta. Qualquer outra reta do plano contm, no mximo, 2 destes pontos. Quantos tringulos podemos formar com os vrtices nestes pontos?

(ITA - 2004) Considere as reaes representadas pelas seguintes equaes qumicas balanceadas: a) C2H5OH(l) + O2(g)2C(s) + 3H2O(g) ∆HI(T); ∆EI(T) b) C2H5OH(l) + 2O2(g) 2CO(g) + 3H2O(l); ∆HII(T); ∆EII(T) sendo ∆H(T) e ∆E(T), respectivamente, a variao da entalpia e da energia interna do sistema na temperatura T. Assuma que as reaes acima so realizadas sob presso constante, na temperatura T, e que a temperatura dos reagentes igual dos produtos. Considere que, para as reaes representadas pelas equaes acima, sejam feitas as seguintes comparaes: I. │∆EI│ = │∆EII│ II. │∆HI│ = │∆HII│ III. │∆HII│ │∆EII│ IV. │∆HI│ │∆EI│ Das comparaes acima, est(o) CORRETA(S)

(ITA - 2004) Duas partculas carregadas com cargas opostas esto posicionadas em uma corda nas posies e, respectivamente. Uma onda transversal e progressiva de equao , presente na corda, capaz de transferir energia para as partculas, no sendo, porm, afetada por elas. Considerando T o perodo da onda, Efa energia potencial eltrica das partculas no instante , e Ei essa mesma energia no instante t = 0, qual a razo ?

(ITA - 2004 - 1a Fase) Considere os metais P, Q , R e S e quatro solues aquosas contendo, cada uma, um dos ons Pp+, Qq+, Rr+, Ss+ (sendo p, q, r, s nmeros inteiros e positivos). Em condies-padro, cada um dos metais foi colocado em contato com uma das solues aquosas e algumas das observaes realizadas podem ser representadas pelas seguintes equaes qumicas: I. qP + pQq+ no ocorre reao. II. rP + pRr+ no ocorre reao. III. rS + sRr+ sR + rSs+. IV. sQ + qSs+ qS + sQq+. Baseado nas informaes acima, a ordem crescente do poder oxidante dos ons Pp+, Qq+, Rr+ e Ss+ deve ser disposta da seguinte forma:

(ITA - 2004 - 1a Fase) Seja x IR e a matriz . Assinale a opo correta.

(ITA - 2004 - 1a Fase) And Now, the Birdcast 1Passing almost unnoticed in the night, billions of birds will fly over the mid-Atlantic states this spring on their 4annual migration northward. A new5Web site will help ornithologists pinpoint 6critical habitat for the feathered 7travelers by combining weather radar 8data with old-fashioned fieldwork. 9Radar has been used to track bird10migrations since around 1940, says 11Steve Kelling, who heads BirdSource, a 12bird database at Cornell University. But the potential payoff grew about 5 years ago when the government began15installing Doppler radar Stations, which 16yield high-resolution three-dimensional 17data. Ornithologists are eager to use 18Doppler to track bird movement, but 19first, they need to calibrate it with data20from the ground. So Cornell, Clemson University, and other groups have launched BirdCast. Every few hours from 1 April to 31 May, radar images of the Philadelphia to25Washington, D. C., area some filtered to remove weather and reveal birds will be posted on the projects Web site (www.birdcast.org). The site will also collect observations30from several hundred citizen-scientists 31(birdwatchers, that is), which will be 32combined with other data, such as chirps 33picked up by acoustic monitors. Kelling 34says the results should reveal the birds35favorite rest stops, highlighting priority 36areas for protection. Eventually, 38BirdCast hopes to go nationwide. SCIENCE Vol 288 7 April 2000 ndices no canto superior esquerdo de uma palavra indica o nmero da linha do texto original. A idia principal abordada pela notcia

(ITA - 2004 - 1a Fase) And Now, the Birdcast 1Passing almost unnoticed in the night, billions of birds will fly over the mid-Atlantic states this spring on their 4annual migration northward. A new5Web site will help ornithologists pinpoint 6critical habitat for the feathered 7travelers by combining weather radar 8data with old-fashioned fieldwork. 9Radar has been used to track bird10migrations since around 1940, says 11Steve Kelling, who heads BirdSource, a 12bird database at Cornell University. But the potential payoff grew about 5 years ago when the government began15installing Doppler radar Stations, which 16yield high-resolution three-dimensional 17data. Ornithologists are eager to use 18Doppler to track bird movement, but 19first, they need to calibrate it with data20from the ground. So Cornell, Clemson University, and other groups have launched BirdCast. Every few hours from 1 April to 31 May, radar images of the Philadelphia to25Washington, D. C., area some filtered to remove weather and reveal birds will be posted on the projects Web site (www.birdcast.org). The site will also collect observations30from several hundred citizen-scientists 31(birdwatchers, that is), which will be 32combined with other data, such as chirps 33picked up by acoustic monitors. Kelling 34says the results should reveal the birds35favorite rest stops, highlighting priority 36areas for protection. Eventually, 38BirdCast hopes to go nationwide. SCIENCE Vol 288 7 April 2000 ndices no canto superior esquerdo de uma palavra indica o nmero da linha do texto original. Considere as seguintes asseres: I. A inteno dos idealizadores do BirdCast que ele se torne um projeto de abrangncia nacional. II. Radares so utilizados em estudos de movimentos migratrios dos pssaros h mais de 60 anos. III. A implantao de estaes de radar Doppler permite a coleta de dados de alta resoluo em trs dimenses. Ento, das afirmaes acima, est(o) correta(s):

(ITA - 2004 - 1a Fase) A figura plana a seguir mostra os elementos de um circuito eltrico. Nesse mesmo plano encontram-se duas espiras interligadas, A e B, de comprimentos relativamente curtos em comparao aos dois fios condutores prximos (CD e EF). A deflexo do ponteiro do micro-ampermetro, intercalado na espira B, s ocorre instantaneamente no momento em que

(ITA - 2004 - 1a Fase) A estrutura molecular da morfina est representada adiante. Assinale a opo que apresenta dois dos grupos funcionais presentes nesta substncia.

(ITA - 2004 - 1a Fase) Considerando as funese, assinale o valor de .

(ITA - 2004 - 1a Fase) And Now, the Birdcast 1Passing almost unnoticed in the night, billions of birds will fly over the mid-Atlantic states this spring on their 4annual migration northward. A new5Web site will help ornithologists pinpoint 6critical habitat for the feathered 7travelers by combining weather radar 8data with old-fashioned fieldwork. 9Radar has been used to track bird10migrations since around 1940, says 11Steve Kelling, who heads BirdSource, a 12bird database at Cornell University. But the potential payoff grew about 5 years ago when the government began15installing Doppler radar Stations, which 16yield high-resolution three-dimensional 17data. Ornithologists are eager to use 18Doppler to track bird movement, but 19first, they need to calibrate it with data20from the ground. So Cornell, Clemson University, and other groups have launched BirdCast. Every few hours from 1 April to 31 May, radar images of the Philadelphia to25Washington, D. C., area some filtered to remove weather and reveal birds will be posted on the projects Web site (www.birdcast.org). The site will also collect observations30from several hundred citizen-scientists 31(birdwatchers, that is), which will be 32combined with other data, such as chirps 33picked up by acoustic monitors. Kelling 34says the results should reveal the birds35favorite rest stops, highlighting priority 36areas for protection. Eventually, 38BirdCast hopes to go nationwide. SCIENCE Vol 288 7 April 2000 ndices no canto superior esquerdo de uma palavra indica o nmero da linha do texto original. Os termos feathered travelers (linhas 6 e 7), it (linha 19) e which (linha 31) referem-se, respectivamente, a

(ITA - 2004 - 1a Fase)O circuito eltrico mostrado na figura constitudo por dois geradores ideais, com 45 V de fora eletromotriz, cada um; dois capacitores de capacitncias iguais a 2 F; duas chaves S e T e sete resistores, cujas resistncias esto indicadas na figura. Considere que as chaves S e T se encontram inicialmente fechadas e que o circuito est no regime estacionrio. Assinale a opocorreta.