Questões - ITA 2009 | Gabarito e resoluções

[ITA - 1 FASE -2009] Um estudante mergulhou uma placa de um metal puro em gua pura isenta de ar, a 25C, contida em um bquer. Aps certo tempo, ele observou a liberao de bolhas de gs e a formao de um precipitado. Com base nessas informaes, assinale a opo que apresenta o metal constituinte da placa.

(ITA - 2009- 2 fase) Suponha que a equao algbrica tenha coeficientes reaistais que as suas onze razes sejam todas simples e da forma em que e osformaram uma progresso aritmtica de razo realConsidere as trs afirmaes abaixo e responda se cada uma delas , respectivamente, verdadeira ou falsa, justificando sua resposta: I.Seento II.Se, ento III.Se ento

[ITA - 1 FASE -2009] Na figura, um ciclista percorre o trecho AB com velocidade escalar mdia de 22,5 km/h e, em seguida, o trecho BC de 3,00 km de extenso. No retorno, ao passar em B, verifica ser de 20,0 km/h sua velocidade escalar mdia no percurso ento percorrido, ABCB. Finalmente, ele chega em A perfazendo todo o percurso de ida e volta em 1,00 h, com velocidade escalar mdia de 24,0 km/h. Assinale o mdulo v do vetor velocidade mdia referente ao percurso ABCB.

[ITA - 1 FASE -2009] (4 questo sobre o texto) Indique o link de onde o pargrafo abaixo foi extrado.

(ITA - 2009 - 1 FASE) Se e,ento, o nmero complexo igual a

[ITA - 1 FASE -2009] Qual o grfico que apresenta a curva que melhor representa o decaimento de uma amostra contendo 10,0 g de um material radioativo ao longo dos anos?

[ITA - 1 FASE -2009] A partir do repouso, um carrinho de montanha russa desliza de uma altura sobre uma rampa de 60 de inclinao e corre 20 m num trecho horizontal antes de chegar em um loop circular, de pista sem atrito. Sabendo que o coeficiente de atrito da rampa e do plano horizontal 1/2, assinale o valor do raio mximo que pode ter esse loop para que o carrinho faa todo o percurso sem perder o contato com a sua pista.

[ITA - 1 FASE -2009] O polinmio de grau 4 (a + 2b + c)x4 + (a + b + c)x3 (a b)x2 + (2a b + c)x + 2 (a + c), com a, b, c IR , uma funo par. Ento, a soma dos mdulos de suas razes igual a

(ITA - 2009- 2 fase) Um determinado concurso realizado em duas etapas. Ao longo dos ltimos anos, 20% dos candidatos do concurso tm conseguido na primeira etapa nota superior ou igual nota mnima necessria para poder participar da segunda etapa. Se tomarmos 6 candidatos dentre os muitos inscritos, qual a probabilidade de no mnimo 4 deles conseguirem nota para participar da segunda etapa?

[ITA - 1 FASE -2009] TEXTILES Smarter Clothes.Europe wants to own the market for fabrics that can monitor you and your environment SALLY MCGRANE/PAVIA AT THE EUCENTRE, A RESEARCH SITE cofounded by the Italian Civil Protection Department in Pavia, Italy, a young engineer dons a firefighters uniform that has been in testing for six months. The first prototype of the Proetex project, the ordinary looking navy blue jacket and pants contain high-tech fabrics that can keep track of a firefighters vital signs, warn him if the fire is too hot up ahead, provide GPS readings of his position and alert the command center if he has passed out. (...) Though the technology was pioneered in the U.S., the Europeans have taken the reins in a bid to revitalize their traditional-textile industry, which has been hammered by Asian competition. We want to develop state-of-the-art know-how that cant be found in Asia, says Andreas Lymberis, a scientific officer with the European Commission who has championed smart textiles. Our purpose is to create a new market. Bringing industry partners like Philips and traditional clothing and textile companies together with university researchers from across the E.U. and Switzerland, Commission-funded teams have already produced prototypes with limited commercial availability, such as a tank top that wirelessly monitors cardiac patients and sports clothes that keep track of breathing. Other projects include fabrics that look and feel normal but are embedded with microcomputers, solar panels and energyharvesting systems, as well as fabrics that measure blood oxygen levels and track biochemicals in sweat and bedsheets that monitor depression. The world market for smart textiles is still small about $ 550 million in revenue in 2008 but that could double by 2010, according to Massachusetts-based venture Development Corp. The challenge is to fit applications to the market, says Lutz Walter, RD manager at Euratex, a group representing the $ 326 billion European clothing-and-textile industry. In the medical field, theres high value added. But to be approved as devices takes 10 years, says Walter. In other areas, its price: How much are consumers going to be willing to pay for a smart jogging shirt or for a baby suit that detects sudden death syndrome? (...) The development of these technologies is currently taking place largely in the biomedical and safety fields, but Annalisa Bonfiglio, a professor of electrical and electronic engineering at the University of Cagliari who coordinates the Proetex project, thinks sports could be the sector where the most potential lies. Sportswear is an extremely powerful means for promoting the acceptance of these new technologies by common people, says Bonfiglio, noting that the technology Proetex develops for rescue workers could easily be used later for sports applications. At the Spaulding Rehabilitation Hospital in Boston, researchers are testing a glove made by Smartex, an Italian smart-materials company, that tracks motor functions in poststroke patients. Smartex founder and University of Pisa biomedicalengineering professor Danilo De Rossi says there is no way of knowing if Europe will maintain its edge. Right now we are leading in this field, he says, since Europe tends to be concerned with medicine, social welfare and the elderly, whereas the U.S. tends to focus on military technology. That could change. But in a business driven by technology rather than price, the Europeans would still have a fighting chance. Time,July 14, 2008 (adapted). Assinale a opo que melhor indica o tema central do texto.

[ITA - 1 FASE -2009] Num experimento, um estudante verificou ser a mesma a temperatura de fuso de vrias amostras de um mesmo material no estado slido e tambm que esta temperatura se manteve constante at a fuso completa. Considere que o material slido tenha sido classificado como: I. Substncia simples pura II. Substncia composta pura III. Mistura homognea euttica IV. Mistura heterognea Ento, das classificaes acima, est(o) ERRADA(S)

[ITA - 1 FASE -2009] Desde os idos de 1930, observaes astronmicas indicam a existncia da chamada matria escura. Tal matria no emite luz, mas a sua presena inferida pela influncia gravitacional que ela exerce sobre o movimento de estrelas no interior de galxias. Suponha que, numa galxia, possa ser removida sua matria escura de massa especfica 0, que se encontra uniformemente distribuda. Suponha tambm que no centro dessa galxia haja um buraco negro de massa M, em volta do qual uma estrela de massa m descreve uma rbita circular. Considerando rbitas de mesmo raio na presena e na ausncia de matria escura, a respeito da fora gravitacional resultante exercida sobre a estrela e seu efeito sobre o movimento desta, pode-se afirmar que

[ITA - 1 FASE -2009] Considere as funes f(x) = x4 + 2x3 2x 1 e g(x) = x2 2x + 1. A multiplicidade das razes no reais da funo composta f g igual a

[ITA - 1 FASE -2009] TEXTILES Smarter Clothes.Europe wants to own the market for fabrics that can monitor you and your environment SALLY MCGRANE/PAVIA AT THE EUCENTRE, A RESEARCH SITE cofounded by the Italian Civil Protection Department in Pavia, Italy, a young engineer dons a firefighters uniform that has been in testing for six months. The first prototype of the Proetex project, the ordinary looking navy blue jacket and pants contain high-tech fabrics that can keep track of a firefighters vital signs, warn him if the fire is too hot up ahead, provide GPS readings of his position and alert the command center if he has passed out. (...) Though the technology was pioneered in the U.S., the Europeans have taken the reins in a bid to revitalize their traditional-textile industry, which has been hammered by Asian competition. We want to develop state-of-the-art know-how that cant be found in Asia, says Andreas Lymberis, a scientific officer with the European Commission who has championed smart textiles. Our purpose is to create a new market. Bringing industry partners like Philips and traditional clothing and textile companies together with university researchers from across the E.U. and Switzerland, Commission-funded teams have already produced prototypes with limited commercial availability, such as a tank top that wirelessly monitors cardiac patients and sports clothes that keep track of breathing. Other projects include fabrics that look and feel normal but are embedded with microcomputers, solar panels and energyharvesting systems, as well as fabrics that measure blood oxygen levels and track biochemicals in sweat and bedsheets that monitor depression. The world market for smart textiles is still small about $ 550 million in revenue in 2008 but that could double by 2010, according to Massachusetts-based venture Development Corp. The challenge is to fit applications to the market, says Lutz Walter, RD manager at Euratex, a group representing the $ 326 billion European clothing-and-textile industry. In the medical field, theres high value added. But to be approved as devices takes 10 years, says Walter. In other areas, its price: How much are consumers going to be willing to pay for a smart jogging shirt or for a baby suit that detects sudden death syndrome? (...) The development of these technologies is currently taking place largely in the biomedical and safety fields, but Annalisa Bonfiglio, a professor of electrical and electronic engineering at the University of Cagliari who coordinates the Proetex project, thinks sports could be the sector where the most potential lies. Sportswear is an extremely powerful means for promoting the acceptance of these new technologies by common people, says Bonfiglio, noting that the technology Proetex develops for rescue workers could easily be used later for sports applications. At the Spaulding Rehabilitation Hospital in Boston, researchers are testing a glove made by Smartex, an Italian smart-materials company, that tracks motor functions in poststroke patients. Smartex founder and University of Pisa biomedicalengineering professor Danilo De Rossi says there is no way of knowing if Europe will maintain its edge. Right now we are leading in this field, he says, since Europe tends to be concerned with medicine, social welfare and the elderly, whereas the U.S. tends to focus on military technology. That could change. But in a business driven by technology rather than price, the Europeans would still have a fighting chance. Time,July 14, 2008 (adapted). De acordo com o texto, a indumentria desenvolvida no Projeto Proetex permite, dentre outras funes, que: I. os sinais vitais e a localizao do usurio sejam monitorados. II. o usurio seja alertado sobre aumento da temperatura externa. III. um possvel desmaio do usurio seja evitado. Est(o) correta(s)

(ITA - 2009- 2 fase) Sejam . Mostre as propriedades abaixo: a) Se AX a matriz coluna nula, para todo , ento A a matriz nula. b) Se A e B so no nulas e tais que AB a matriz nula, ento det A = detB = 0.