Adding heat to a liquid causes which of the following physical changes?

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 ?

What properties of a moving object are used in determining the object's energy of motion

Two students, each riding bicycles, start from the same apartment building and ride to the same building on campus, but each takes a different route. the first student rides 1100 m due east and then turns due north and travels another 1430 m before arriving at the destination. the second student heads due north for 1930 m and then turns and heads directly toward the destination.at the turning point, how far is the second student from the destination?