Questões de f - ITA | Gabarito e resoluções

(ITA - 2015 - 1 FASE) Seja A, B e C os subconjuntos de definidos por ,e. Ento, o conjunto

Uma espira quadrada, feita de um material metálico homogêneo e rígido, tem resistência elétrica R e é solta em uma região onde atuam o campo gravitacional g = – gez e um campo magnético Inicialmente a espira encontra-se suspensa, conforme a figura, com sua aresta inferior no plano xy num ângulo α com o eixo y, e o seu plano formando um ângulo β com z. Ao ser solta, a espira tende a

(ITA - 2015 - 1 FASE) Na frase She said she had been driving home from work the night before, and she found herself behind a man in a convertible (linhas 3 e 4), a formao correta quanto ao uso do discurso direto :

Um muon de meia-vida de 1,5 μs é criado a uma altura de 1 km da superfície da Terra devido à colisão de um raio cósmico com um núcleo e se desloca diretamente para o chão. Qual deve ser a magnitude mínima da velocidade do muon para que ele tenha 50% de probabilidade de chegar ao chão?

(ITA - 2015 - 1 FASE) THE MAN IN THE CONVERTIBLE One morning, well after I was diagnosed with cancer, I got an email from Robbee Kosak, 7Carnegie Mellons vice president for advancement. She told me a story. 22She said she had been driving home from work the night before, and 11she found herself behind a man in a convertible. 1It was a warm, gorgeous, early-spring evening, and the man had his top down and all his windows lowered. His arm was hanging over 8the drivers side door, and his fingers were tapping along to the music on his radio. His head was bobbing along, too, 13as the wind blew through his hair. Robbee changed lanes and pulled a little closer. From the side, she could see that the man had a slight smile on his face, the kind of 16absentminded smile a person might have when hes all alone, happy in his own thoughts. 12Robbee found herself thinking: Wow, this is the epitome of a person appreciating this day and this moment. The convertible 18eventually turned the corner, and thats when Robbee got a look at 9the mans full face. Oh my God, she said to herself. Its Randy Pausch! 2She was so struck by the sight of me. She knew that my cancer diagnosis was grim. And yet, 14as she wrote in her email, 3she was moved by how contented I seemed. In this private moment, 4I was 19obviously in high spirits. Robbee wrote in her email: You can never know how much that glimpse of you made my day, reminding me of what life is all about. I read 10Robbees email several times. I came to look at it 15as a feedback loop of sorts. It has not always been easy to stay positive through my cancer treatment. When you have a dire medical issue, its tough to know how youre 20really faring emotionally. I had wondered whether a part of me was acting when I was with other people. Maybe at times I forced myself to appear strong and upbeat. Many cancer patients feel obliged to put up a brave front. Was I doing that, too? But Robbee had come upon me in an unguarded moment. Id like to think she saw me as I am. 5She 21certainly saw me as I was that evening. Her mail was just a paragraph, but it meant a great deal to me. 6She had given me a window into myself. I was still fully 17engaged. I still knew life was good. I was doing OK. Fonte: PAUSCH, R. The last lecture. New York, Hyperion, 2008. p. 64 - 65. Com relao s escolhas lexicais do autor no texto, pode-se afirmar que

(ITA - 2015) Borbulha-se gs cloro em soluo aquosa diluda de hidrxido de sdio a 25C. Assinale a opo que contm apenas produtos clorados resultantes.

(ITA - 2015 - 1 FASE) Sejam e nmeros reais tais que , , + ]0; 2[ e satisfazem as equaes e Ento, o menor valor de cos( + ) igual a

(ITA - 2015 - 1 FASE) Seja C uma circunferncia tangente simultaneamente s retas r : 3x + 4y - 4 = 0 e s : 3x + 4y - 19 = 0. A rea do crculo determinado por C igual a

(ITA - 2015) Uma pequena esfera metlica, de massa m e carga positiva q, lanada verticalmente para cima com velocidade inicial v0 em uma regio onde h um campo eltrico de mdulo E, apontado para baixo, e um gravitacional de mdulo g, ambos uniformes. A mxima altura que a esfera alcana :

(ITA - 2015 - 1 FASE) A empresa Legacy Effects

(ITA - 2015) Um tubo em forma de U de seo transversal uniforme, parcialmente cheio at uma altura h com um determinado lquido, posto num veculo que viaja com acelerao horizontal, o que resulta numa diferena de altura z do lquido entre os braos do tubo interdistantes de um comprimento L. Sendo desprezvel o dimetro do tubo em relao L, a acelerao do veculo dada por

(ITA - 2015 - 1 FASE) Considere todos os tringulos retngulos com os lados medindo ,e.Dentre esses tringulos, o de maior hipotenusa tem seu menor ngulo, em radianos, igual a

(ITA - 2015 - PROPOSTA REDAO)

(ITA - 2015) Luz, que pode ser decomposta em componentes de comprimento de onda com 480 nm e 600 nm incide verticalmente em uma cunha de vidro com ngulo de abertura = 3,00 e ndice de refrao de 1,50 conforme a figura, formando linhas de interferncia destrutivas. Qual a distncia entre essas linhas?

Seja (a1, a2, a3, ...) a sequncia definida da seguinte forma: a1 = 1, a2 = 1 e an = an-1+ an-2 para n 3.Considere as afirmaes a seguir: I. Existem trs termos consecutivos, ap, ap+1, ap+2, que, nesta ordem, formam uma progresso geomtrica. II. a7 um nmero primo. III. Se n mltiplo de 3, ento an par. (so) verdadeira(s).