Answer :
Answer:
[tex] A_T = \left[\begin{array}{cc}-cos(2/3 \pi)&sen(2/3 \pi)\\sen(2/3\pi)&cos(2/3\pi)\end{array}\right][/tex]
Step-by-step explanation:
60 degree is equivalent to 2/3 π. The linear transformation of a counterclockwise rotation of angle 2/3 π is
[tex]R(2/3 \, \Pi) = \left[\begin{array}{cc}cos(2/3 \pi)&-sen(2/3 \pi)\\sen(2/3\pi)&cos(2/3\pi)\end{array}\right][/tex]
On the other hand, the reflection throught the Y-axis is given by the linear transformation
[tex] RY(x,y) = (-x,y) [/tex]
Hence its associated matrix is
[tex] A_{RY} = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex]
And the composition is given by
[tex] A_T = A_{RY} * R(2/3 \, \Pi) = \left[\begin{array}{cc}-cos(2/3 \pi)&sen(2/3 \pi)\\sen(2/3\pi)&cos(2/3\pi)\end{array}\right][/tex]