Questões - ITA 2007 | Gabarito e resoluções

(ITA - 2007 - 1a Fase) Considere: um retngulo cujos lados medem B e H, um tringulo issceles em que a base e a altura medem, respectivamente, B e H, e o cı́rculo inscrito neste tringulo. Se as reas do retngulo, do tringulo e do cı́rculo, nesta ordem, formam uma progresso geomtrica, ento B/H uma raiz do polinmio

(ITA - 2007 - 1Fase) TEXTO I A text familiar to many, George Orwells classic satirehas cropped upon school reading lists ever since the year of its creation. Few readers canfailto be touched by the tragedy within, by its wonderful synthesis of unthreatening symbolism and incisive criticism. This familiarity is convenientsince, as an adaptation, Animal Farm spends too little time on the details of time and place.Instead, directors Joy Batchelor and John Halas thrust us directly into the depression that is Manor Farm, briefly explaining the situation with pictures and narration by Gordon Heath. (...) Sadly, Batchelor and Halas make it vital to have read Orwells biting satire on Soviet history before viewing Animal Farm, just to know whats been left out. As it is, the film grasps the superficial aspects of Orwells allegoric fable without his deeper message. In missing so badly, were left with an impressive attempt that never matches up to its birthright. TEXTO II Power corrupts, but absolute power corrupts absolutely - and this is vividly and eloquently proved in Orwells short novel. Animal Farm is a simple fable of great symbolic value, and as Orwell himself explained: It is the history of a revolution that went wrong. The novel can be seen as the historical analysis of the causes of the failure of communism, or as a mere fairy-tale; in any case it tells a good story that aims to prove that human nature and diversitypreventpeoplefrombeing equal and happy, or at least equally happy. (...) In Animal Farm, Orwell describes how power turned the pigs from simple comrades to ruthless dictators who managed to walk on two legs, and carry whips. The story may be seen as an analysis of the Soviet regime, or as a warning against political power games of an absolute nature and totalitarianism in general. For this reason, the story ends with a hair- raising warning to all humankind: The creatures outside looked from pig to man, and from man to pig, and from pig to man again: but already it was impossible to say which was which. TEXTO III When the farms prize-winning pig, Old Major, calls a meeting of all the animals of Manor Farm, he tells them that he has had a dream in which mankind is gone, and animals are free to live in peace and harmony. (...) . When Old Major dies, (...) Snowball and Napoleon assume command, and turn his dream into a full-fledged philosophy. One night, the starved animals suddenly revolt and drive the farmer Mr. Jones, his wife, and his pet raven off the farm and take control. The farm is renamed Animal Farm as the animals work towards a future utopia. The Seven Commandments of the new philosophy of Animalism are written on the wall of a barn for all to read, the seventh and most important ofwhichis that all animals are equal (...). Many years pass, and the pigs learn to walk upright, carry whips, and wear clothes. The Seven Commandments are reduced to a single phrase: All animals are equal, but some animals are more equal than others. Napoleon holds a dinner party for the pigs, and the humans of the area (in the adjacent Foxwood Farm run by Mr. Pilkington), who congratulate Napoleon on having the most hard working animals in the country on the least feed. Napoleon announces his alliance with the humans against the labouring classes of both worlds. The animals discover this when they overhear Napoleons conversations and finallyrealizethat a change has come over the ruling pigs. During a poker match, an argumentbreaks outbetween Napoleon and Mr. Pilkington when they both play an Ace of Spades, and the animalsrealizehow they cannot tell the difference between the pigs and the humans. No Texto III o termo which em the seventh and most important of which is that... refere-se a

(ITA - 2007 - 1a Fase) Dois bqueres, X e Y, contm, respectivamente, volumes iguais de solues aquosas: concentrada e diluda de cloreto de sdio na mesma temperatura. Dois recipientes hermeticamente fechados, mantidos mesma temperatura constante, so interconectados por uma vlvula, inicialmente fechada, cada qual contendo um dos bqueres. Aberta a vlvula, aps o restabelecimento do equilbrio qumico, verifica-se que a presso de vapor nos dois recipientes Pf. Assinale a opo que indica a curva no grfico abaixo que melhor representa a quantidade de massa de gua transferida (Qgua) ao longo do tempo (t) de um recipiente para o outro desde o instante em que a vlvula aberta at o restabelecimento do equilbrio qumico.

(ITA - 2007 - 1a Fase) Na experincia idealizada na figura, um halterofilista sustenta, pelo ponto M, umconjunto em equilbrio esttico composto de uma barra rgida e uniforme, de um peso P1 = 100N na extremidade a 50 cm de M, e de um peso P2 = 60 N, na posio x2 indicada. A seguir, omesmo equilbrio esttico verificado dispondo-se, agora, o peso P2 na posio original de P1 ,passando este posio de distncia x1 = 1,6 x2 da extremidade N. Sendo de 200 cm o comprimento da barra e g = 10 m/s a acelerao da gravidade, a massada barra de:

(ITA - 2007 - 1a Fase) Se as medidas dos lados de um tringulo obtusngulo esto em progresso geomtrica de razo r, ento r pertence ao intervalo

(ITA - 2007 - 1a Fase) Considere duas placas X e Y de mesma rea e espessura. A placa X constituda de ferro com uma das faces recoberta de zinco. A placa Y constituda de ferro com uma das faces recoberta de cobre. As duas placas so mergulhadas em bqueres, ambos contendo gua destilada aerada. Depois de um certo perodo, observa-se que as placas passaram por um processo de corroso, mas no se verifica a corroso total de nenhuma das faces dos metais. Considere que sejam feitas as seguintes afirmaes a respeito dos ons formados em cada um dos bqueres: I. Sero formados ons Zn2+ no bquer contendo a placa X. II. Sero formados ons Fe2+ no bquer contendo a placa X. III. Sero formados ons Fe2+ no bquer contendo a placa Y. IV. Sero formados ons Fe3+ no bquer contendo a placa Y. V. Sero formados ons Cu2+ no bquer contendo a placa Y. Ento, das afirmaes anteriores, esto CORRETAS

(ITA - 2007 - 1a Fase) TEXTO I A text familiar to many, George Orwells classic satirehas cropped upon school reading lists ever since the year of its creation. Few readers canfail to be touched by the tragedy within, by its wonderful synthesis of unthreatening symbolism and incisive criticism. This familiarity is convenient since, as an adaptation, Animal Farm spends too little time on the details of time and place.Instead, directors Joy Batchelor and John Halas thrust us directly into the depression that is Manor Farm, briefly explaining the situation with pictures and narration by Gordon Heath. (...) Sadly, Batchelor and Halas make it vital to have read Orwells biting satire on Soviet history before viewing Animal Farm, just to know whats been left out. As it is, the film grasps the superficial aspects of Orwells allegoric fable without his deeper message. In missing so badly, were left with an impressive attempt that never matches up to its birthright. TEXTO II Power corrupts, but absolute power corrupts absolutely - and this is vividly and eloquently proved in Orwells short novel. Animal Farm is a simple fable of great symbolic value, and as Orwell himself explained: It is the history of a revolution that went wrong. The novel can be seen as the historical analysis of the causes of the failure of communism, or as a mere fairy-tale; in any case it tells a good story that aims to prove that human nature and diversitypreventpeoplefrombeing equal and happy, or at least equally happy. (...) In Animal Farm, Orwell describes how power turned the pigs from simple comrades to ruthless dictators who managed to walk on two legs, and carry whips. The story may be seen as an analysis of the Soviet regime, or as a warning against political power games of an absolute nature and totalitarianism in general. For this reason, the story ends with a hair- raising warning to all humankind: The creatures outside looked from pig to man, and from man to pig, and from pig to man again: but already it was impossible to say which was which. TEXTO III When the farms prize-winning pig, Old Major, calls a meeting of all the animals of Manor Farm, he tells them that he has had a dream in which mankind is gone, and animals are free to live in peace and harmony. (...) . When Old Major dies, (...) Snowball and Napoleon assume command, and turn his dream into a full-fledged philosophy. One night, the starved animals suddenly revolt and drive the farmer Mr. Jones, his wife, and his pet raven off the farm and take control. The farm is renamed Animal Farm as the animals work towards a future utopia. The Seven Commandments of the new philosophy of Animalism are written on the wall of a barn for all to read, the seventh and most important ofwhichis that all animals are equal (...). Many years pass, and the pigs learn to walk upright, carry whips, and wear clothes. The Seven Commandments are reduced to a single phrase: All animals are equal, but some animals are more equal than others. Napoleon holds a dinner party for the pigs, and the humans of the area (in the adjacent Foxwood Farm run by Mr. Pilkington), who congratulate Napoleon on having the most hard working animals in the country on the least feed. Napoleon announces his alliance with the humans against the labouring classes of both worlds. The animals discover this when they overhear Napoleons conversations and finallyrealizethat a change has come over the ruling pigs. During a poker match, an argumentbreaks outbetween Napoleon and Mr. Pilkington when they both play an Ace of Spades, and the animalsrealizehow they cannot tell the difference between the pigs and the humans. No final do Texto III, o autor afirma que os animais no conseguiam mais diferenciar os homens dos porcos. Qual das opes abaixo, com frases encontradas no Texto II, faz observao semelhante?

(ITA - 2007 - 1a Fase) No arranjo mostrado na figura com duas polias, o fio inextensvel e sem pesosustenta a massa M e, tambm, simetricamente, as duas massas m, em equilbrio esttico. Desprezando o atrito de qualquer natureza, o valor h da distncia entre os pontos P e Q vale:

(ITA - 2007 - 1a Fase) TEXTO I A text familiar to many, George Orwells classic satirehas cropped upon school reading lists ever since the year of its creation. Few readers canfail to be touched by the tragedy within, by its wonderful synthesis of unthreatening symbolism and incisive criticism. This familiarity is convenient since, as an adaptation, Animal Farm spends too little time on the details of time and place.Instead, directors Joy Batchelor and John Halas thrust us directly into the depression that is Manor Farm, briefly explaining the situation with pictures and narration by Gordon Heath. (...) Sadly, Batchelor and Halas make it vital to have read Orwells biting satire on Soviet history before viewing Animal Farm, just to know whats been left out. As it is, the film grasps the superficial aspects of Orwells allegoric fable without his deeper message. In missing so badly, were left with an impressive attempt that never matches up to its birthright. TEXTO II Power corrupts, but absolute power corrupts absolutely - and this is vividly and eloquently proved in Orwells short novel. Animal Farm is a simple fable of great symbolic value, and as Orwell himself explained: It is the history of a revolution that went wrong. The novel can be seen as the historical analysis of the causes of the failure of communism, or as a mere fairy-tale; in any case it tells a good story that aims to prove that human nature and diversitypreventpeoplefrombeing equal and happy, or at least equally happy. (...) In Animal Farm, Orwell describes how power turned the pigs from simple comrades to ruthless dictators who managed to walk on two legs, and carry whips. The story may be seen as an analysis of the Soviet regime, or as a warning against political power games of an absolute nature and totalitarianism in general. For this reason, the story ends with a hair- raising warning to all humankind: The creatures outside looked from pig to man, and from man to pig, and from pig to man again: but already it was impossible to say which was which. TEXTO III When the farms prize-winning pig, Old Major, calls a meeting of all the animals of Manor Farm, he tells them that he has had a dream in which mankind is gone, and animals are free to live in peace and harmony. (...) . When Old Major dies, (...) Snowball and Napoleon assume command, and turn his dream into a full-fledged philosophy. One night, the starved animals suddenly revolt and drive the farmer Mr. Jones, his wife, and his pet raven off the farm and take control. The farm is renamed Animal Farm as the animals work towards a future utopia. The Seven Commandments of the new philosophy of Animalism are written on the wall of a barn for all to read, the seventh and most important ofwhichis that all animals are equal (...). Many years pass, and the pigs learn to walk upright, carry whips, and wear clothes. The Seven Commandments are reduced to a single phrase: All animals are equal, but some animals are more equal than others. Napoleon holds a dinner party for the pigs, and the humans of the area (in the adjacent Foxwood Farm run by Mr. Pilkington), who congratulate Napoleon on having the most hard working animals in the country on the least feed. Napoleon announces his alliance with the humans against the labouring classes of both worlds. The animals discover this when they overhear Napoleons conversations and finallyrealizethat a change has come over the ruling pigs. During a poker match, an argumentbreaks outbetween Napoleon and Mr. Pilkington when they both play an Ace of Spades, and the animalsrealizehow they cannot tell the difference between the pigs and the humans. A expresso break out em destaque no Texto III significa

(ITA - 2007 - 1a Fase) Uma bala de massa m e velocidade v0 disparada contra um bloco de massa M, que inicialmente se encontra em repouso na borda de um poste de altura h, conforme mostra a figura. A bala aloja-se no bloco que, devido ao impacto, cai no solo. Sendo g a acelerao da gravidade, e no havendo atrito e nem resistncia de qualquer outra natureza, o mdulo da velocidade com que o conjunto atinge o solo vale

(ITA - 2007 - 1a Fase) Embrulhar frutas verdes em papel jornal favorece o seu processo de amadurecimento devido ao acmulo de um composto gasoso produzido pelas frutas. Assinale a opo que indica o composto responsvel por esse fenmeno.

(ITA - 2007 - 1a Fase) Sejam x, y e z nmeros reais positivos tais que seus logaritmos numa dada base n so nmeros primos satisfazendo logn (xy) = 49, logn (x/z) = 44. Ento logn (xyz) igual a

(ITA - 2007 - 1a Fase) Projetado para subir com velocidade mdia constante a uma altura de 32 m em40 s, um elevador consome a potncia de 8,5 kW de seu motor. Considere que seja de 370 kg a massa do elevador vazio e a acelerao da gravidade g = 10 m/s. Nessas condies, o nmero mximo de passageiros, de 70 kg cada um, a ser transportado pelo elevador :

(ITA - 2007 - 1a Fase) De acordo com o texto do cartaz, considere as seguintes afirmaes: I. o V SBPMat uma conferncia internacional realizada anualmente na rea de Cincias dos Materiais e Engenharia. II. o evento tem por objetivo promover discusses sobre temas ligados pesquisa em Materiais. III. estaro presentes no evento engenheiros e cientistas de vrias partes do mundo, no apenas do Brasil. Ento, est(o) correta(s)

(ITA - 2007 - 1a Fase) Assinale a opo que apresenta um sal que, quando dissolvido em gua, produz uma soluo aquosa cida.