Questões - ITA 2017 | Gabarito e resoluções

(ITA - 2017 - 1 FASE) Sejam X e Y dois conjuntos finitos com X Y e X Y . Considere as seguintes afirmaes: Existe uma bijeo f : X Y . Existe uma funo injetora g : Y X. O nmero de funes injetoras f : X Y igual ao nmero de funes sobrejetoras g : Y X. (so) verdadeira(s)

(ITA - 2017 - 1FASE) Pode-se utilizar metais de sacrifcio para proteger estruturas de ao (tais como pontes, antenas e cascos de navios) da corroso eletroqumica. Considere os seguintes metais: Alumnio Magnsio Paldio Sdio Zinco Assinale a opo que apresenta o(s) metal(is) de sacrifcio que pode(m) ser utilizado(s).

(ITA - 2017 - 2 FASE) Considere as retas de equaes e , em que a, b, c so reais. Sabendo que r e s so perpendiculares entre si, com r passando por (0, 1) e s,por (2 , 4), determine a rea do tringulo formado pelas retas r, s e o eixo x.

(ITA - 2017 - 1 FASE) Ondas gravitacionais foram previstas por Einstein em 1916 e diretamente detectadas pela primeira vez em 2015. Sob determinadas condies, um sistema girando com velocidade angular irradia tais ondas com potncia proporcional a em que G a constante de gravitao universal; c, a velocidade da luz e Q, uma grandeza que tem unidade em kg.m2. Assinale a opo correta.

(ITA - 2017 - 2 FASE) Em queda livre a partir do repouso, um im atravessa longitudinalmente o interior de um tubo de plstico, sem tocar-lhe as paredes, durante um intervalo de tempo t. Caso este tubo fosse de metal, o tempo para essa travessia seria maior, igual ou menor que t? Justifique sua resposta.

(ITA - 2017- 2 Fase) Gs cloro borbulhado em uma soluo aquosa concentrada de NaOH a quente, obtendo-se dois nions X e Y. a) Quais so estas espcies X e Y? b) Com a adio de soluo aquosa de nitrato de prata poder-se-ia identificar estes nions? Justifique sua resposta utilizando equaes qumicas e descrevendo as caractersticas do(s) produto(s) formado(s).

(ITA - 2017 - 1 FASE) A questo refere-se ao texto a seguir: FRAYING AT THE EDGES: A LIFE-CHANGING DIAGNOSIS IT BEGAN WITH what she saw in the bathroom mirror. On a dull morning, Geri Taylor padded into the shiny bathroom of her Manhattan apartment. She casually1 checked her reflection in the mirror, doing her daily inventory. Immediately, she stiffened with fright. Huh? What? She didnt recognize herself. She gazed saucer-eyed at her image, thinking: Oh, is this what I look like? No, thats not me. Whos that in my mirror? This was in late 2012. She was 69, in her early months getting familiar with retirement. For some time she had experienced the sensation of clouds coming over her, mantling thought. There had been a few hiccups at her job. She had been a nurse who climbed the rungs to health care executive. Once, she was leading a staff meeting6 when she had no idea what she was talking about, her mind like a stalled engine that wouldnt turn over. Fortunately2 I was the boss and I just said, Enough of that; Sally, tell me what youre up to,she would say of the episode. Certain mundane tasks stumped her. She told her husband, Jim Taylor, that the blind in the bedroom was broken. He showed her she was pulling the wrong cord. Kept happening. Finally3, nothing else working, he scribbled on the adjacent wall which cord was which. Then there was the day she got off the subway at 14th Street and Seventh Avenue unable to figure out why she was there. So, yes, she had had inklings7 that something was going wrong with her mind. She held tight to thesethoughts. She even hid her suspicions from Mr. Taylor, who chalked up her thinning8 memory to the infirmities of age. I thought she was getting like me,he said. Ihad been forgetful for 10 years. But to not recognize her own face! To Ms. Taylor, this was the drop-dead momentwhen she had to accept a terrible truth. She wasnt just seeing the twitches of aging but the early4 fumes of the disease. She had no further issues with mirrors, but there was no ignoring9 that something important had happened. She confided her fears to her husband and made an appointment with a neurologist. Before then I thought I could fake it,she would explain. This convinced me I had to come clean. In November 2012, she saw the neurologist who was treating her migraines. He listened to hersymptoms, took blood, gave her the Mini Mental State Examination, a standard cognitive test made up of aset of unremarkable questions and commands. (For instance, she was asked to count backward from 100 in intervals of seven; she had to say the phrase: No ifs, ands or buts; she was told to pick up a piece of paper, fold it in half and place it on the floor beside her.) He told her three common words, said he was going to ask her them in a little bit. He emphasized this by pointing10 a finger at his head remember those words. That simple. Yet when he called for them, she knew only one: Beach. In her mind, she would go on to associate it with the doctor, thinking of him as Dr.Beach. He gave a diagnosis of mild cognitive impairment, a common precursor to Alzheimers disease. Thefirst label put on what she had. Even then, she understood it was the footfall of what would come. Alzheimers had struck her father, a paternal aunt and a cousin. She long suspected it would eventually5 find her. Fonte: http://www.nytimes.com/interactive/2016/05/01/nyregion/living-with-alzheimers.html?action=clickcontentCollection=Americasmodule=Trendingversion=Fullregion= Marginaliapgtype=article. (acesso em 1/05/2016). Quanto ao gnero textual, o texto pode ser classificado como

(ITA - 2017- 2 Fase) Ambos os ons sulfeto e sulfito reagem, em meio cido, com o on bromato, provocando o aparecimento de uma colorao no meio reacional. a) Escreva as equaes qumicas balanceadas que representam as reaes que provocam o aparecimento de colorao no meio reacional. b) Escreva a equao qumica balanceada que representa a reao envolvendo o sulfito quando h excesso do agente redutor. Nestas condies, explique o que ocorre com a colorao do meio reacional.

(ITA - 2017 - 1 FASE) A questo refere-se ao texto a seguir: FRAYING AT THE EDGES: A LIFE-CHANGING DIAGNOSIS IT BEGAN WITH what she saw in the bathroom mirror. On a dull morning, Geri Taylor padded into the shiny bathroom of her Manhattan apartment. She casually1 checked her reflection in the mirror, doing her daily inventory. Immediately, she stiffened with fright. Huh? What? She didnt recognize herself. She gazed saucer-eyed at her image, thinking: Oh, is this what I look like? No, thats not me. Whos that in my mirror? This was in late 2012. She was 69, in her early months getting familiar with retirement. For some time she had experienced the sensation of clouds coming over her, mantling thought. There had been a few hiccups at her job. She had been a nurse who climbed the rungs to health care executive. Once, she was leading a staff meeting6 when she had no idea what she was talking about, her mind like a stalled engine that wouldnt turn over. Fortunately2 I was the boss and I just said, Enough of that; Sally, tell me what youre up to,she would say of the episode. Certain mundane tasks stumped her. She told her husband, Jim Taylor, that the blind in the bedroom was broken. He showed her she was pulling the wrong cord. Kept happening. Finally3, nothing else working, he scribbled on the adjacent wall which cord was which. Then there was the day she got off the subway at 14th Street and Seventh Avenue unable to figure out why she was there. So, yes, she had had inklings7 that something was going wrong with her mind. She held tight to thesethoughts. She even hid her suspicions from Mr. Taylor, who chalked up her thinning8 memory to the infirmities of age. I thought she was getting like me,he said. Ihad been forgetful for 10 years. But to not recognize her own face! To Ms. Taylor, this was the drop-dead momentwhen she had to accept a terrible truth. She wasnt just seeing the twitches of aging but the early4 fumes of the disease. She had no further issues with mirrors, but there was no ignoring9 that something important had happened. She confided her fears to her husband and made an appointment with a neurologist. Before then I thought I could fake it,she would explain. This convinced me I had to come clean. In November 2012, she saw the neurologist who was treating her migraines. He listened to hersymptoms, took blood, gave her the Mini Mental State Examination, a standard cognitive test made up of aset of unremarkable questions and commands. (For instance, she was asked to count backward from 100 in intervals of seven; she had to say the phrase: No ifs, ands or buts; she was told to pick up a piece of paper, fold it in half and place it on the floor beside her.) He told her three common words, said he was going to ask her them in a little bit. He emphasized this by pointing10 a finger at his head remember those words. That simple. Yet when he called for them, she knew only one: Beach. In her mind, she would go on to associate it with the doctor, thinking of him as Dr.Beach. He gave a diagnosis of mild cognitive impairment, a common precursor to Alzheimers disease. Thefirst label put on what she had. Even then, she understood it was the footfall of what would come. Alzheimers had struck her father, a paternal aunt and a cousin. She long suspected it would eventually5 find her. Fonte: http://www.nytimes.com/interactive/2016/05/01/nyregion/living-with-alzheimers.html?action=clickcontentCollection=Americasmodule=Trendingversion=Fullregion= Marginaliapgtype=article. (acesso em 1/05/2016). Quanto narrativa, o texto apresentado

(ITA - 2017 - 1 FASE) O nmero de solues da equao , com ,

(ITA - 2017 - 2 FASE) Determine todos os valores reais de xque satisfazem a inequao

(ITA - 2017 - 1 FASE) A reao do mercrio metlico com excesso de cido sulfrico concentrado a quente produz um gs mais denso do que o ar. Dois teros deste gs so absorvidos e reagem completamente com uma soluo aquosa de hidrxido de sdio, formando 12,6 g de um sal. A soluo de cido sulfrico utilizada tem massa especfica igual a 1,75 gcm-3 e concentrao de 80 % em massa. Assinale a alternativa que apresenta o volume consumido da soluo de cido sulfrico, em cm3. Dados de massa molar (g/mol): Na = 23 ; S = 32 ; O = 16 ; H = 1.

(ITA - 2017 - 2 FASE) Suponha que a atmosfera de Vnus seja composta dos gases CO2, N2, Ar, Ne e He, em equilbrio trmico a uma temperatura T = 735 K. a) Determine a razo entre a velocidade quadrtica mdia das molculas de cada gs e a velocidade de escape nesse planeta. b) Que concluso pode ser obtida sobre a provvel concentrao desses gases nessa atmosfera? Obs.: Considere Vnus com o raio igual ao da Terra e a massa igual a 0,810 vezes a desta.

(ITA - 2017 - 1 FASE) Um basto rgido e uniforme, de comprimento L, toca os pinos P e Q fixados numa parede vertical, interdistantes de a, conforme a figura. O coeficiente de atrito entre cada pino e o basto , e o ngulo deste com a horizontal . Assinale a condio em que se torna possvel o equilbrio esttico do basto.

(ITA - 2017 - 1 FASE) Um frasco fechado contm dois gases cujo comportamento considerado ideal: hidrognio molecular e monxido de nitrognio. Sabendo que a presso parcial do monxido de nitrognio igual a 3/5 da presso parcial do hidrognio molecular, e que a massa total da mistura de 20 g, assinale a alternativa que fornece a porcentagem em massa do hidrognio molecular na mistura gasosa.