Answer:
Option C. 225 degrees
Step-by-step explanation:
The given matrix is
[tex]\begin{bmatrix}-\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\\ -\frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2}\end{bmatrix}[/tex]
which is in the form of
[tex]\begin{bmatrix}cos\phi & -sin\phi \\ cos\phi & sin\phi \end{bmatrix}[/tex]
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.
