Questões - ITA 2001 | Gabarito e resoluções

(ITA - 2001 - 1a Fase) Considere as funes , e. Se a tal que h(f(a)) + h(g(a)) =/4, ento f(a) - g(a) vale:

(ITA - 2001 - 1a Fase) Um objeto linear de altura h est assentado perpendicularmente no eixo principalde um espelho esfrico, a 15cm de seu vrtice. A imagem produzida direita e tem altura deh/5. Este espelho

(ITA - 2001 - 1a Fase) Assinale a alternativa ERRADA relativa comparao do ponto de ebulio de algumas substncias orgnicas.

(ITA - 2001 - 1a Fase) (...) Ever since Dad had returned from his life at sea he had been interested in robots. Maybe that in itself wasnt so strange, but with Dad it didnt end there. He was convinced that one day science would be able to create artificial people. By this, he didnt just mean those dumb metal robots with red and green flashing lights and hollow voices. Oh no, Dad believed that science would one day be able to create real thinking human beings, like us. And there was more -he also believed that, fundamentally, human beings are artificial objects. (...) Just imagine if all this suddenly came alive, Hans Thomas,he said. Imagine if these Lego figures suddenly began to toddle around among the plastic houses. What would we do then?(...) Basically, we ourselves are such Lego figures. The Solitaire Mystery-J. Gaardner- p.8 O trecho acima foi extrado de uma histria:

(ITA - 2001 - 1a Fase)Uma partcula estsubmetida a uma fora com as seguintes caractersticas: seu mdulo proporcional ao mdulo da velocidade da partcula e atua numa direo perpendicular aquela do vetor velocidade. Nestas condies, a energia cintica da partcula deve

(ITA - 2001 - 1a Fase) O conjunto de todos os valores dempara os quais a funo est definida e no-negativa para todo x real :

(ITA - 2001 - 1a Fase) Uma determinada substncia apresenta as seguintes propriedades fsico-qumicas: I. O estado fsico mais estvel a 25C e 1atm o slido. II. No estado slido apresenta estrutura cristalina. III. A condutividade eltrica praticamente nula no estado fsico mais estvel a 25C e 1atm. IV. A condutividade eltrica alta no estado lquido. A alternativa relativa substncia que apresenta todas as propriedades acima a

(ITA -2001 - 1a Fase) A parte imaginria de ((1 + cos 2x) + i sen 2x)b, b inteiro positivo, x real,

(ITA - 2001 - 1a Fase) A calcinao de 1,42 g de uma mistura slida constituda de CaCO3 e MgCO3 produziu um resduo slido que pesou 0,76 g e um gs. Com estas informaes, qual das opes a seguir a relativa afirmao CORRETA? Dados Massas molares (g/mol): CaCO3 = 100,09; CaO = 56,08; MgCO3 = 84,32; MgO = 40,31

(ITA - 2001 - 1a Fase) No circuito eltrico da figura, os vrios elementos tm resistncias R1, R2 e R3conforme indicado. Sabendo que 2xR3= R1, para que a resistncia equivalente entre os pontos Ae B da associao da figura seja igual a 2xR2 a razo r=R2/R1 deve ser:

(ITA - 2001 - 1a Fase) (...) Ever since Dad had returned from his life at sea he had been interested in robots. Maybe that in itself wasnt so strange, but with Dad it didnt end there. He was convinced that one day science would be able to create artificial people. By this, he didnt just mean those dumb metal robots with red and green flashing lights and hollow voices. Oh no, Dad believed that science would one day be able to create real thinking human beings, like us. And there was more -he also believed that, fundamentally, human beings are artificial objects. (...) Just imagine if all this suddenly came alive, Hans Thomas,he said. Imagine if these Lego figures suddenly began to toddle around among the plastic houses. What would we do then?(...) Basically, we ourselves are such Lego figures. The Solitaire Mystery-J. Gaardner- p.8 Assinale a alternativa que melhor corresponde ao texto anterior:

(ITA - 2001 - 1a Fase) Considere as semirreaes representadas pelas semiequaes a seguir e seus respectivos potenciais padro de eletrodo: E0 = - 0,44 V E0 = 0,26 V E0 = 0,80 V Com base nas informaes acima, qual das opes a seguir relativa equao qumica de uma reao que dever ocorrer quando os reagentes, nas condies padro, forem misturados entre si?

(ITA -2001 - 1a Fase) O polinmio com coeficientes reais P(x) = x5 + a4x4 + a3x3 + a2x2 + a1x + a0 tem duas razes distintas, cada uma delas com multiplicidade 2, e duas de suas razes so 2 e i. Ento, a soma dos coeficientes igual a:

(ITA - 2001 - 1a Fase) (...) Ever since Dad had returned from his life at sea he had been interested in robots. Maybe that in itself wasnt so strange, but with Dad it didnt end there. He was convinced that one day science would be able to create artificial people. By this, he didnt just mean those dumb metal robots with red and green flashing lights and hollow voices. Oh no, Dad believed that science would one day be able to create real thinking human beings, like us. And there was more -he also believed that, fundamentally, human beings are artificial objects. (...) Just imagine if all this suddenly came alive, Hans Thomas,he said. Imagine if these Lego figures suddenly began to toddle around among the plastic houses. What would we do then?(...) Basically, we ourselves are such Lego figures. The Solitaire Mystery-J. Gaardner- p. 8 Assinale a alternativa que melhor expressa o significado da frase Ever since Dad had returned from his life at sea he had been interested in robots.

(ITA - 2001 - 1a Fase) Duas partculas tm massas iguais a m e cargas iguais a Q. Devido a suainterao eletrosttica, elas sofrem uma fora F quando esto separadas de uma distncia d. Em seguida, estas partculas so penduradas, a partir de um mesmo ponto, por fios decomprimento L e ficam equilibradas quando a distncia entre elas d1. A cotangente do nguloque cada fio forma com a vertical, em funo de m, g, d, d1, F e L,