Answered

Join the growing community of curious minds on IDNLearn.com and get the answers you need. Find the answers you need quickly and accurately with help from our knowledgeable and experienced experts.

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

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]

Sagot :

GinnyAnsweridn
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]
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.