multiple choice question with math solution give me plz...

2 points (d) Coordinate vector of the vector , with respect to the basis {{}] . [ ]} is O (1/3,-5/3) AT O (1, 1) AT O ( 4, 2 ) "T 2 points (a) The kernel of the transformation T(x) = (2x1 - X2, x2 + X3,5x1 ) is {(1 01)^T, (0 1 0) "T} O ((1, 1, 1) "T} O {(0,0,0)"T} 6 points Rotate the rectangle having vertices (0,0), (3,0), (3,2) and (0,2) in an angle /3 in the counter clockwise direction. Show detail of your calculations and the figure of both of the rectangles. 1 Add file