(a) Without using mathematical tables or calculator, evaluate \(\frac{\frac{3}{2}\log 27 - 3\log 5\sqrt{5}}{\log 0.6}\) (b) Two linear transformations A and...

(a) Without using mathematical tables or calculator, evaluate \(\frac{\frac{3}{2}\log 27 - 3\log 5\sqrt{5}}{\log 0.6}\)

(b) Two linear transformations A and B in the \(O_{xy}\) plane, are defined by :

\(A : (x, y)   (x + 2y, -x + y)\)

\(B : (x, y)   (2x + 3y, x + 2y)\).

(i) Write down the matrices A and B; (ii) Find the image of the point P(-2, 2) under the linear transformation A followed by B.