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2. Fie forma pătratică \( \varphi: \mathbf{R}^{3} \rightarrow \mathbf{R}, \varphi(x)=2 x_{1}^{2}+5 x_{2}^{2}+x_{3}^{2}-2 x_{1} x_{2}+2 x_{1} x_{3}-4 x_{2} x_{3} \) pentru orice \( x=\left(x_{1}, x_{2}, x_{3}\right) \in \mathbf{R}^{3} \). 2.1. Să se scrie forma biliniară simetrică asociată şi matricea asociată (în raport cu baza canonică). 2.2. Să se aducă forma pătratică la o formă canonică, precizând baza formei canonice şi rangul formei. 2.3. Să se indice, dacă există, trei vectori \( u, v, w \operatorname{din} \mathbf{R}^{3} \) pentru care \( \varphi(u)=0 \) şi \( u \neq 0 \), \( \varphi(v)>0, \varphi(w)<0 \). Este \( \varphi \) pozitiv definită?
Romania Jan 21, 2025
How can teens demonstrate good physical fitness to their families? by keeping their rooms tidy by flossing their teeth every day by saying please and thank you by taking the stairs instead of the elevator
United States Jan 21, 2025
21 TIME REMANING Rosario is concerned about her physical fitness. She has been recording in her journal the number of minutes she exercises each day for several days. She learns that she exercises an average of 15 minutes per day. Which would most likely help Rosario increase the amount of time she exercises? joining a local sports league increasing her amount of screen time increasing the number of healthy snacks she eats socializing with her peers
United States Jan 21, 2025
Michael believes that a piece of equipment he bought will quickly sculpt his abdominal muscles. What can this belie be best identified as? a fitness fad a safety plan a workout routine an equipment manual
United States Jan 21, 2025
The Egyptian life spirit or life force is called the ra ka serdab ankh
United States Jan 21, 2025
Which personal goal should Abigail incorporate into her plan for healthy eating? Exercise and eat a well-balanced diet only when she wants. Look for food options with a large amount of refined grains. Eliminate foods high in protein from her diet. Increase intake of foods rich in soluble and insoluble fiber.
United States Jan 21, 2025
What is the best reason to wear PPE? To block hazards from your body Your supervisor insists It's comfortable OSHA may be visiting
United States Jan 21, 2025
The freezing point of water corresponds to ... A. 273 K B. 32 K C. -32 K D. 0 K
United States Jan 21, 2025
What is the next step after gathering information when making smart food choices? Decide if help is needed. Take personal responsibility. Review the decision made. Identify alternative food choices.
United States Jan 21, 2025
3. Найдите координаты вектора \[ \vec{p}=\frac{1}{3} \vec{a}-2 \vec{b}+\frac{1}{2} \vec{c}, \] \[ \begin{array}{l}\text { если } \\ \vec{a}\{-1 ; 2 ;-3\}, \quad \vec{b}\{4 ; 3 ; 7\}, \quad \vec{c}\{-6 ; 1 ; 5\}\end{array} \]
Russia Jan 21, 2025
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