When a non-isotropic material is heated, the fractional increase in length is different along different directions. a rectangular plate with lengths l1 = 6.1 cm and l2 = 6.0 cm is made from such a material. in the direction along l1, the coefficient of linear expansion is α1 = 10 × 10−5 k−1 . in the direction of l2, the coefficient of linear expansion is α2 = 40 × 10−5 k−1 . the plate is heated until it becomes a perfect square. what is the area of the square?

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 ?

The specific heat of silver is 0.057 calories/gram°c. if 10.0 grams of silver were heated and the temperature of the sample changed by 20.0°c, how many calories of heat energy were absorbed by the sample?

Player kicks a soccer ball from ground level and sends it flying at an angle of 30 degrees at a speed of 26 m/s. what is the horizontal velocity component of the ball to the nearest tenth of a m/s?