What are ways to improve the design of this experiment? Check all that apply

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

Does work output exceed work input when a machine is used? a) yes, it does, as machines create energy. b) it depends on the type of machine used. c) no, it doesn’t, as machines are inefficient. d) no, it doesn’t, as machines cannot create energy.

A2-kg bowling ball is 2.5 meters off the ground on a post when it falls. just before it reaches the ground, it is traveling 7 m/s. assuming that there is no air resistance, which statement is true?