Answer:
The answer is (2,1)
Step-by-step explanation:
Given a vector in the plane, we can describe the rotation as a function :
X is the vector
T is the function that represents the rotation
[tex]T(X)=AX[/tex]
Where A is the rotation matrix
The rotation matrix about the origin in counterclockwise sense for an angle ''a'' is :
[tex]A=\left[\begin{array}{cc}cos(a)&-sin(a)\\sin(a)&cos(a)\end{array}\right][/tex]
If we replace ''a'' by 90 ⇒
[tex]\left[\begin{array}{cc}cos(90)&-sin(90)\\sin(90)&cos(90)\\\end{array}\right][/tex]
[tex]A=\left[\begin{array}{cc}0&-1\\1&0\\\end{array}\right][/tex]
If we want to rotate the vector D = (1,-2) :
[tex]T(D)=AD=\left[\begin{array}{cc}0&-1\\1&0\\\end{array}\right]\left[\begin{array}{c}1&-2\end{array}\right]=\left[\begin{array}{c}2&1\end{array}\right][/tex]
The rotation of the vector (1,-2) about the origin for an angle of 90 and in counterclockwise sense is (2,1)
