An ideal gas in a piston-cylinder assembly undergoes two processes in series. During the first process 1-2, from state 1 to state 2, 500 kJ of heat is transferred to the gas while the gas does 800 kJ of work on the piston. The second process, from state 2 to state 3, is a constant pressure compression at 400 kPa during which 450 kJ of heat is lost through the cylinder walls. The internal energy contained in the cylinder gas at states 1 and 3 is 2000 kJ and 3500 kJ, respectively.

Sketch the process on P-V diagram and deternine the total work transfer.

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west