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Which of the following units is used by meteorologists to measure air pressure? View Available Hint(s) \( \begin{array}{l}\text { pounds per square inch } \\ \text { grams per cubic centimeter } \\ \text { millimeters } \\ \text { millibars } \\ \text { milliliters }\end{array} \)

Ask by Newton Potter. in the United States
Jan 19,2025

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Meteorologists use **millibars** to measure air pressure.

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Meteorologists primarily use millibars to measure air pressure, which is a unit that quantifies the weight of the air above a given point. One standard atmosphere is equivalent to 1013.25 millibars, making it a crucial aspect of weather forecasting and understanding atmospheric conditions. In practical terms, air pressure readings in millibars help meteorologists predict weather patterns. For example, low-pressure systems often indicate stormy weather, while high-pressure systems are associated with clear skies. Understanding these variations can significantly improve our ability to plan outdoor activities or prepare for unexpected weather changes!

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Numéro d'étudiant : 22007890 La qualité de la rédaction sera prise en compte. Exercice 1. Soit \[ \mathcal{B}=\left\{\left[\begin{array}{ll} 1 & 0 \\ 0 & 0 \end{array}\right],\left[\begin{array}{ll} 0 & 1 \\ 0 & 0 \end{array}\right],\left[\begin{array}{ll} 0 & 0 \\ 1 & 0 \end{array}\right],\left[\begin{array}{ll} 0 & 0 \\ 0 & 1 \end{array}\right]\right\} \] la base canonique de \( \operatorname{Mat}_{2}(\mathbb{R}) \) et soit \( f: \operatorname{Mat}_{2}(\mathbb{R}) \rightarrow \operatorname{Mat}_{2}(\mathbb{R}) \) l'endomorphisme de \( \operatorname{Mat}_{2}(\mathbb{R}) \) tel que, en base canonique, \[ f\left(\left[\begin{array}{ll} x_{1} & x_{2} \\ x_{3} & x_{4} \end{array}\right]\right)=\left(\left[\begin{array}{cc} x_{1}+2 x_{3} & 2 x_{1}-x_{2}+4 x_{3}-2 x_{4} \\ -x_{3} & -2 x_{3}+x_{4} \end{array}\right]\right) \] (a) Montrer que \[ A=\mu_{\mathcal{B}, \mathcal{B}}(f)=\left(\begin{array}{cccc} 1 & 0 & 2 & 0 \\ 2 & -1 & 4 & -2 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & -2 & 1 \end{array}\right) \] où \( \mu_{\mathcal{B}, \mathcal{B}}(f) \) est la matrice associée à \( f \) dans la base canonique. \( ~ \) trer que l'endomorphisme \( f \) est diagonalisable. Déterminer une base \( \mathcal{B}^{\prime} \) de \( \operatorname{Mat}_{2}(\mathbb{R}) \) formée de vecteurs propres de \( \operatorname{Mat}_{2}(\mathbb{R}) \), la matrice de changement de base \( P:=\mu_{\mathcal{B}^{\prime}, \mathcal{B}}\left(\operatorname{Id}_{\mathrm{Mat}_{2}(\mathbb{R})}\right) \) et la matrice diagonale \( D:=\mu_{\mathcal{B}^{\prime}, \mathcal{B}^{\prime}}(f) \) telles que \[ \mu_{\mathcal{B}^{\prime}, \mathcal{B}^{\prime}}(f)=\left(\mu_{\mathcal{B}^{\prime}, \mathcal{B}}\left(\operatorname{Id}_{\operatorname{Mat}_{2}(\mathbb{R})}\right)\right)^{-1} \mu_{\mathcal{B}, \mathcal{B}}(f) \mu_{\mathcal{B}^{\prime}, \mathcal{B}}\left(\operatorname{Id}_{\operatorname{Mat}_{2}(\mathbb{R})}\right) \] Autrement dit, \[ D=P^{-1} A P \] où \( A=\mu_{\mathcal{B}, \mathcal{B}}(f) \).
Other France Jan 22, 2025
Numéro d'étudiant : La qualité de la rédaction sera prise en compte. Exercice 1. Soit \[ \mathcal{B}=\left\{\left[\begin{array}{ll} 1 & 0 \\ 0 & 0 \end{array}\right],\left[\begin{array}{ll} 0 & 1 \\ 0 & 0 \end{array}\right],\left[\begin{array}{ll} 0 & 0 \\ 1 & 0 \end{array}\right],\left[\begin{array}{ll} 0 & 0 \\ 0 & 1 \end{array}\right]\right\} \] la base canonique de \( \operatorname{Mat}_{2}(\mathbb{R}) \) et soit \( f: \operatorname{Mat}_{2}(\mathbb{R}) \rightarrow \operatorname{Mat}_{2}(\mathbb{R}) \) l'endomorphisme de \( \operatorname{Mat}_{2}(\mathbb{R}) \) tel que, en base canonique, \[ f\left(\left[\begin{array}{ll} x_{1} & x_{2} \\ x_{3} & x_{4} \end{array}\right]\right)=\left(\left[\begin{array}{cc} x_{1}+2 x_{3} & 2 x_{1}-x_{2}+4 x_{3}-2 x_{4} \\ -x_{3} & -2 x_{3}+x_{4} \end{array}\right]\right) \] (a) Montrer que \[ A=\mu_{\mathcal{B}, \mathcal{B}}(f)=\left(\begin{array}{cccc} 1 & 0 & 2 & 0 \\ 2 & -1 & 4 & -2 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & -2 & 1 \end{array}\right) \] où \( \mu_{\mathcal{B}, \mathcal{B}}(f) \) est la matrice associée à \( f \) dans la base canonique. (b) Déterminer le polynôme caractéristique \( \chi_{f}(x) \). (c) Déterminer les valeurs propres de \( f \), leurs multiplicités algébriques et montrer que l'endomorphisme \( f \) est diagonalisable. (d) Déterminer une base \( \mathcal{B}^{\prime} \) de \( \operatorname{Mat}_{2}(\mathbb{R}) \) formée de vecteurs propres de \( \operatorname{Mat}_{2}(\mathbb{R}) \), la matrice de changement de base \( P:=\mu_{\mathcal{B}^{\prime}, \mathcal{B}}\left(\operatorname{Id}_{\operatorname{Mat}_{2}(\mathbb{R})}\right) \) et la matrice diagonale \( D:=\mu_{\mathcal{B}^{\prime}, \mathcal{B}^{\prime}}(f) \) telles que \[ \mu_{\mathcal{B}^{\prime}, \mathcal{B}^{\prime}}(f)=\left(\mu_{\mathcal{B}^{\prime}, \mathcal{B}}\left(\operatorname{Id}_{\operatorname{Mat}_{2}(\mathbb{R})}\right)\right)^{-1} \mu_{\mathcal{B}, \mathcal{B}}(f) \mu_{\mathcal{B}^{\prime}, \mathcal{B}}\left(\operatorname{Id}_{\operatorname{Mat}_{2}(\mathbb{R})}\right) \] Autrement dit, \[ D=P^{-1} A P \] où \( A=\mu_{\mathcal{B}, \mathcal{B}}(f) \).
Other France Jan 22, 2025
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