Answer:
R = [tex]\left[\begin{array}{ccc}1&0&0\\0&cos30&-sin30\\0&sin30&cos30\end{array}\right][/tex][tex]\left[\begin{array}{ccc}cos 60&-sin60&0\\sin60&cos60&60\0&0&1\end{array}\right][/tex]
Explanation:
The mappings always involve a translation and a rotation of the matrix. Therefore, the rotation matrix will be given by:
Let [tex]\theta[/tex] and [tex]\alpha[/tex] be the the angles 60⁰ and 30⁰ respectively
that is [tex]\theta[/tex] = 60⁰ and
[tex]\alpha[/tex] = 30⁰
The matrix is given by the following expression:
[tex]\left[\begin{array}{ccc}1&0&0\\0&cos30&-sin30\\0&sin30&cos30\end{array}\right][/tex][tex]\left[\begin{array}{ccc}cos 60&-sin60&0\\sin60&cos60&60\0&0&1\end{array}\right][/tex]
The angles can be evaluated and left in the surd form.
