Questões - ITA 2009 | Gabarito e resoluções

[ITA - 1 FASE -2009] Suponha que os coeficientes reais a e b da equao x4 + ax3 + bx2 + ax + 1 = 0 so tais que a equao admite soluo no real r com .Das seguintes afirmaes: I. A equao admite quatro razes distintas, sendo todas no reais. II. As razes podem ser duplas. III. Das quatro razes, duas podem ser reais. (so) verdadeira( s )

(ITA - 2009- 2 fase) Sabendo quepara algum ,determine sen x.

[ITA - 1 FASE -2009] Diagramas causais servem para representar relaes qualitativas de causa e efeito entre duas grandezas de um sistema. Na sua construo, utilizamos figuras como para indicar que o aumento da grandeza r implica aumento da grandeza s e para indicar que o aumento da grandeza r implica diminuio da grandeza s. Sendo a a acelerao, v a velocidade e x a posio, qual dos diagramas abaixo melhor representa o modelamento do oscilador harmnico?

[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 biomedical engineering 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: I. a tecnologia hoje utilizada para o desenvolvimento de tecidos inteligentes para uniformes de bombeiros poder ser facilmente adaptada para roupas de esportistas. II. h consumidores dispostos a pagar qualquer preo por uma pea de roupa infantil que sinalize a doena morte-sbita. III. em breve, os asiticos passaro a dominar o mercado de tecidos inteligentes, hoje nas mos dos europeus. Est(o) correta(s)

[ITA - 1 FASE -2009] Assinale a afirmao CORRETA a respeito do ponto de ebulio normal (PE) de algumas substncias.

[ITA - 1 FASE -2009] (4 questo sobre o texto) Assinale a opo em que o termo II NO pode substituir o termo I no texto.

[ITA - 1 FASE -2009] O diagrama temperatura (T) versus volume (V) representa hipoteticamente as transformaes pelas quais um gs ideal no estado 1 pode atingir o estado 3. Sendo U a variao de energia interna e q a quantidade de calor trocado com a vizinhana, assinale a opo com a afirmao ERRADA em relao s transformaes termodinmicas representadas no diagrama.

[ITA - 1 FASE -2009] Se as solues da equao algbrica 2x3 ax2 + bx + 54 = 0, com coeficientes a, b IR, b 0, formam, numa determinada ordem, uma progresso geomtrica, ento, igual a

[ITA - 1 FASE -2009] Uma balsa tem o formato de um prisma reto de comprimento L e seo transversal como vista na figura. Quando sem carga, ela submerge parcialmente at a uma profundidade h0. Sendo a massa especfica da gua e g a acelerao da gravidade, e supondo seja mantido o equilbrio hidrosttico, assinale a carga P que a balsa suporta quando submersa a uma profundidade h1.

(ITA - 2009- 2 fase) Considere as n retas , em que os coeficientes , em ordem crescente de i, formam uma progresso aritmtica de razoq 0.Se e a reta tangencia a circunferncia de equao x + y= 25, determine o valor de q:

[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 biomedical engineering 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 indica o projeto, ou prottipo, de uso de tecido inteligente que NO mencionado no texto.

[ITA - 1 FASE -2009] Dados A M3x2 (IR) e b M3x1 (IR), dizemos que X0 M2x1 (IR) a melhor aproximao quadrtica do sistema AX = b quando assume o menor valor possvel. Ento, dado o sistema a sua melhor aproximao quadrtica

[ITA - 1 FASE -2009] Considere hipoteticamente duas bolas lanadas de um mesmo lugar ao mesmo tempo: a bola 1, com velocidade para cima de 30 m/s, e a bola 2, com velocidade de 50 m/s formando um ngulo de 30 com a horizontal. Considerando g = 10 m/s2, assinale a distncia entre as bolas no instante em que a primeira alcana sua mxima altura.

[ITA - 1 FASE -2009] Considere os tomos hipotticos neutros V, X, Y e Z no estado gasoso. Quando tais tomos recebem um eltron cada um, as configuraes eletrnicas no estado fundamental de seus respectivos nions so dadas por: V- (g): [gs nobre] ns2np6nd10(n + 1)s2(n + 1)p6 X- (g): [gs nobre] ns2np6 Y- (g): [gs nobre] ns2np6nd10(n + 1)s2(n + 1)p3 Z- (g): [gs nobre] ns2np3 Nas configuraes acima, [gs nobre] representa a configurao eletrnica no diagrama de Linus Pauling para o mesmo gs nobre, e n o mesmo nmero quntico principal para todos os nions. Baseado nessas informaes, CORRETO afirmar que

[ITA - 1 FASE -2009] (6 questo sobre o texto) De acordo com o texto: I. estima-se que a renda do mercado mundial de tecidos inteligentes poder atingir 1.1 bilho de dlares em aproximadamente dois anos. II. Smartex uma empresa italiana que foi fundada por um professor universitrio. III. a Comisso Europia subsidiou uma equipe composta pela Philips, por empresas tradicionais das reas txtil e de vesturio e por pesquisadores universitrios americanos e suos. Est(o) correta(s)