Is a vector necessarily changed if it is rotated through an angle?

Two polaroids are kept crossed to each other. Now one of them is rotated through an angle of 45^(@) . The percentage of incident light now transmitted through the system is

A bar magnet is placed in the position of stable equilibrium in a uniform magnetic field of induction B. If it is rotated through an angle 180^@ , then the work done is.......(M = Magnetic Dipole moment of Bar magnet)

The vector hati+xhatj+3hatk is rotated through an angle theta and doubled in magnitude, then it becomes 4hati+(4x-2)hatj+2hatk . Then values of x are

The vector hati+xhatj+3hatk is rotated through an angle theta and doubled in magnitude then it becomes 4hati+(4x-2)hatj+2hatk . The values of x are

A wheel has angular acceleration of 3" rad/s"^(2) and initial angular speed of 2.00 rad/s. In a time 2 sec. it has rotated through an angle……….rad of :

The point represented by the complex nuber (2-i) is rotated about origin through an angle (pi)/(2) in the clockwise direction, the new position of point is

A vector a has components a_1,a_2,a_3 in a right handed rectangular cartesian coordinate system OX,OY,OZ the coordinate axis is rotated about z axis through an angle pi/2 . The components of a in the new system

Are fand g both necessarily onto, if gof is onto?

A horizontal ray of light passes through a prism of index 1.50 and apex angle 4^(@) and then strikes a vertical mirror , as shown in the figure. Through what angle must the mirror be rotated if after reflection the ray is to be horizontal?