T R2 rightarrow R2 rotates points about the origin through

T : R^2 rightarrow R^2 rotates points (about the origin) through 3pi /2 radians (counterclockwise).

Solution

The final matrix is of order 2X1 since the point will have 2 coordinates x and y, hence the order of T matrix will be of dimensions of 2X2

Rotation matrix of order 2X2 is given by

This matrix will provide the shift and will not enhance the magnitude,

Reason: |Det(2X2)| = cos^2(x) + sin^2(x) = 1

Hence it will not change the magnitude and just provide the rotation effect, now for getting 3pi/2 radians rotations substitute x=3pi/2, we get

Hence the matrix will be equal to

cos(x)	-sin(x)
sin(x)	cos(x)