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The vector matrix [tex]\left[\begin{array}{l}-3 \\ -5\end{array}\right][/tex] is rotated at different angles. Match the angles of rotation with the vector matrices they produce.

- [tex]\frac{\pi}{2}[/tex]
- [tex]\frac{3 \pi}{4}[/tex]
- [tex]\frac{5 \pi}{3}[/tex]
- [tex]\frac{5 \pi}{6}[/tex]
- [tex]\frac{3 \pi}{2}[/tex]
- [tex]\frac{4 \pi}{3}[/tex]



Answer :

GinnyAnswer
Let's look at each given angle of rotation and match it with the corresponding resulting vector matrix.

1. [tex]\(\frac{\pi}{2}\)[/tex] radians:
- The result is [tex]\(\begin{bmatrix} 5 \\ -3 \end{bmatrix}\)[/tex]

2. [tex]\(\frac{3\pi}{4}\)[/tex] radians:
- The result is [tex]\(\begin{bmatrix} 5.65685425 \\ 1.41421356 \end{bmatrix}\)[/tex]

3. [tex]\(\frac{5\pi}{3}\)[/tex] radians:
- The result is [tex]\(\begin{bmatrix} -5.83012702 \\ 0.09807621 \end{bmatrix}\)[/tex]

4. [tex]\(\frac{5\pi}{6}\)[/tex] radians:
- The result is [tex]\(\begin{bmatrix} 5.09807621 \\ 2.83012702 \end{bmatrix}\)[/tex]

5. [tex]\(\frac{3\pi}{2}\)[/tex] radians:
- The result is [tex]\(\begin{bmatrix} -5 \\ 3 \end{bmatrix}\)[/tex]

6. [tex]\(\frac{4\pi}{3}\)[/tex] radians:
- The result is [tex]\(\begin{bmatrix} -2.83012702 \\ 5.09807621 \end{bmatrix}\)[/tex]

Here are the pairs:
- [tex]\(\frac{\pi}{2}\)[/tex] matches with [tex]\(\begin{bmatrix} 5 \\ -3 \end{bmatrix}\)[/tex]
- [tex]\(\frac{3\pi}{4}\)[/tex] matches with [tex]\(\begin{bmatrix} 5.65685425 \\ 1.41421356 \end{bmatrix}\)[/tex]
- [tex]\(\frac{5\pi}{3}\)[/tex] matches with [tex]\(\begin{bmatrix} -5.83012702 \\ 0.09807621 \end{bmatrix}\)[/tex]
- [tex]\(\frac{5\pi}{6}\)[/tex] matches with [tex]\(\begin{bmatrix} 5.09807621 \\ 2.83012702 \end{bmatrix}\)[/tex]
- [tex]\(\frac{3\pi}{2}\)[/tex] matches with [tex]\(\begin{bmatrix} -5 \\ 3 \end{bmatrix}\)[/tex]
- [tex]\(\frac{4\pi}{3}\)[/tex] matches with [tex]\(\begin{bmatrix} -2.83012702 \\ 5.09807621 \end{bmatrix}\)[/tex]

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