What is a polarizer and an analyser?

The intensity of transmitted light when a polaroid sheet is placed between two crossed polaroids at $22.5^{\circ}$ from the polarization axis of one of the polaroids is (where $I_0$ is the intensity of polarized light after passing through the first polaroid):

Two polarizers are oriented with their principal planes making an angle of $60^{\circ}$ with each other. The percentage of incident unpolarized light which passes through the system is: (in $\%$)

Two Nicols are oriented with their principal planes making an angle of $60^\circ$. The percentage of incident unpolarized light which passes through the system is......$\%$

When light of an unknown polarization is examined with a polaroid,it is found to exhibit maximum intensity $I_0$ along the $y$-axis and minimum intensity $\frac{2I_0}{3}$ along the $x$-axis. The intensity transmitted through a polaroid with pass axis at $45^{\circ}$ to the $y$-axis (in the $x$-$y$ plane) is:

In the figure,suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also,let the center disk be rotated on the common axis with an angular speed $\omega$. If unpolarized light is incident on the left disk with an intensity $I_{max}$,the intensity of the beam emerging from the right disk is given by: