How did Ptolemy adapt the geocentric model so he could account for the motion of the planets? ANSWER ASAP

In a heat engine if 1000 j of heat enters the system the piston does 500 j of work, what is the final internal energy of the system if the initial energy was 2000 j ?

An object's buoyant force and weight mean the same thing. a. trueb. false

Light from a sodium lamp passes through a diffraction grating that has 1000 slits per millimeter. the interference pattern is viewed on a screen 1.000 m behind the grating. the first (m = 1) two bright yellow fringes that are visible are 0.7288 m and 0.7300 m from the central maximum. what are the wavelengths of these two fringes?