Question

What degree of rotation is represented on this matrix

Answer 1

The degree of rotation represented on a matrix is measured in angles, such as degrees or radians.

Step-by-step explanation:

The degree of rotation represented on a matrix is typically measured in terms of angles, such as degrees or radians. In order to determine the degree of rotation on a matrix, you need to identify the angle of rotation.

If the matrix is rotated clockwise, the angle is considered negative (-). If the matrix is rotated counterclockwise, the angle is considered positive (+).

For example, if a matrix is rotated 90 degrees counterclockwise, the degree of rotation would be +90°.

Answer 2

Option B is correct

the degree of rotation is,
`-90^(\circ)`

Step-by-step explanation:

A rotation matrix is a matrix that is used to perform a rotation in Euclidean space.

To find the degree of rotation using a standard rotation matrix i.e,

`R = \begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}`

Given the matrix:
`\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}`

Now, equate the given matrix with standard matrix we have;

`\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}` =
`\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}`

On comparing we get;

`\cos \theta = 0` and
`-\sin \theta =1`

As,we know:

• 
  `\cos \theta = \cos(-\theta)`

• 
  `\sin(-\theta) = -\sin \theta`

`\cos \theta = \cos(90^(\circ)) = \cos( -90^(\circ))`

we get;

`\theta = -90^(\circ)`

and

`\sin \theta =- \sin (90^(\circ)) = \sin ( -90^(\circ))`

we get;

`\theta = -90^(\circ)`

Therefore, the degree of rotation is,
`-90^(\circ)`