Question

Which angle of rotation is determined by the matrix below? (pictured above)

Answer 1

Answer:

Option C. 225 degrees

Step-by-step explanation:

The given matrix is

$\begin{bmatrix}-\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\\ -\frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2}\end{bmatrix}$

which is in the form of

$\begin{bmatrix}cos\phi & -sin\phi \\ cos\phi & sin\phi \end{bmatrix}$

where ∅ is the angle of rotation of any vector.

By comparing the elements of first column of two matrices given

Value of cos ∅ = -√2/2

∅ = either 225° or 315°

and it is also given that (sin ∅) = -√2/2 or sin ∅ = -√2/2

Therefore ∅ = either 225° or 315°

Now sin ∅ = -√2/2

∅ = either 135° or 225°

So the common angle is 225°

Now it's confirmed that measurement of angle ∅ = 225°

Option C. 225° degrees is the answer.

Answer 2

I think the answer is C hope this would help you