Which angle of rotation is determined by the matrix below? (pictured above) a. 45 degrees b. 135 degrees c. 225 degrees d. 315 degrees

Option C. 225 degrees

Step-by-step explanation:

The given matrix is

which is in the form of

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.

5

step-by-step explanation:

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.