Q.What will you observe if, instead of rotating only one of the polaroids, you rotate both polaroids simultaneously in the same direction?

Since light is a transverse wave, its electric field can point in any direction within the plane perpendicular to its direction of travel. Ordinary light from a source is UNPOLARIZED -- a random mixture of many independent wave trains, each with its own random field direction in that plane. A POLARIZER (e.g. a Polaroid sheet) transmits only the field component along one fixed direction (its polarizing axis), producing PLANE POLARIZED light with a single, well-defined oscillation direction; the plane containing the propagation direction and the surviving field is the plane of vibration, and the plane perpendicular to that (but still containing the ray) is the plane of polarization. …