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Home Question Bank Other Archive 2024 December 07

Other Questions from Dec 07,2024

Browse the Other Q&A Archive for Dec 07,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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4- The operator \( A \) defined on \( \mathbb{R}^{3} \) has an eigen-plane with eigenvalue 2 and an eigen-direction (perpendicular to the plane) with eigenvalue \( 1 / 2 \). Without any explicit calculation, draw the effect of \( A \) on the unit sphere. What is the volume of the resulting region? Which of the following is a federal law that criminalizes illegal activities committed by organized crime members? The Violent Crime Control and Law Enforcement law The Civil Rights Act The Hate Crime Statistics Act Racketeer Influenced and Corrupt Organizations law 1. Determine cual de los siguientes subconjuntos dados forman una base para \( \mathbb{R}^{3} \). i) \( \{(1,1,1),(1,2,3),(0,1,0)\} \) ii) \( \{(1,1,2),(2,2,0),(3,4,-1)\} \). 2. Sean \( S=\left\{v_{1}, v_{2}, v_{3}\right\} \) y \( T=\left\{w_{1}, w_{2}, w_{3}\right\} \) bases para \( \mathbb{R}^{3} \) donde \[ v_{1}=(1,0,1), \quad v_{2}=(-1,0,0), \quad v_{3}=(0,1,2) \] \[ w_{1}=(-1,1,0), \quad w_{2}=(1,2,-1), \quad w_{3}=(0,1,0) \] y Además, sea \( v \in \mathbb{R}^{3} \) con \( v=(1,3,8) \) i) Determine el vector de coordenadas de \( v \) con respecto a las bases \( S \) y \( T \) ii) Calule la matriz transición \( P_{S \leftarrow T} \) de la base T a la base \( S \) iii) Verifique que \( [v] S=P_{S \leftarrow T}[v]_{T} \). 1. Determine cual de los siguientes subconjuntos dados forman una base para \( \mathbb{R}^{3} \). i) \( \{(1,1,1),(1,2,3),(0,1,0)\} \). ii) \( \{(1,1,2),(2,2,0),(3,4,-1)\} \). Exprese al vector \( v=(2,1,3) \) como combinación lineal de los vectores de cada conjunto que sea una base para \( \mathbb{R}^{3} \). 2. Sean \( S=\left\{v_{1}, v_{2}, v_{3}\right\} \) y \( T=\left\{w_{1}, w_{2}, w_{3}\right\} \) bases para \( \mathbb{R}^{3} \) donde \[ v_{1}=(1,0,1), \quad v_{2}=(-1,0,0), \quad v_{3}=(0,1,2) \] y \[ w_{1}=(-1,1,0), \quad w_{2}=(1,2,-1), \quad w_{3}=(0,1,0) \] Además, sea \( v \in \mathbb{R}^{3} \) con \( v=(1,3,8) \). i) Determine el vector de coordenadas de \( v \) con respecto a las bases \( S \) y \( T \). ii) Calule la matriz transición \( P_{S \leftarrow T} \) de la base T a la base \( S \). iii) Verifique que \( [v] S=P_{S \leftarrow T}[v]_{T} \). 6. Elabora una breve historia en la que expliques de manera muy clara y sencilla el concepto de oferta, su importancia y su funcionamiento. Para esto, puedes utilizar algún ejemplo de tu día a día. \begin{tabular}{l} A researcher conducts an experiment to determine whether \\ moderate doses of St. Johns Wort have any effect of \\ memory for college students. For this study, what is the \\ independent variable? \\ \hline a. The amount of St. Johns Wort given to each participant \\ \hline b. The memory score for each participant \\ \hline c. The group of college students \\ \hline d. \\ \hline\end{tabular} Let \( G \) be the simple group of order 168 , what is number of subgroup of order 7. \( \begin{array}{ll}\text { (a) } 8 & \text { (b) } 7 \\ \text { (c) } 15 & \text { (d) } 22\end{array} \) 3. Let \( G \) be the simple group of order 168 , what is number of subgroul order 7 . \( \begin{array}{ll}\text { (a) } 8 & \text { (b) } 7 \\ \text { (c) } 15 & \text { (d) } 22\end{array} \) Select the correct statements pertaining to the dot product. \( \square \) The dot product vector is the diagonal in a parallelogram formed by the two vectors \( \vec{u} \) and \( \vec{v} \). \( \square \) The dot product of two vectors is always a scalar. \( \square \) The dot product of orthogonal vectors is always 0 . \( \square \) The dot product of orthogonal vectors is always 1 .
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