Spin and matrices (20 points total) (10 pts) using the matrix representation of the sa-α-x, y, z operators, compute the matrix representation of s2operator. remember, s is a vector operator, so its square is understood as a dot product of two vectors (each of which is a matrix) (10 pts) using the matrix representation of the s2 operator and the vector representation of the α and b spin states, show that the latter are the eigenvectors of s2 and compute the corresponding eigenvalues.

What is the radius of the circular path ofa charged particle in a magnetic field?

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. a small hole is made in the side of each tank at the same depth 1.57 m below the liquid surface, but the hole in tank 2 has 2.49 times the cross-sectional area of the hole in tank 1. (a) what is the ratio ρ1/ρ2 of the densities of the liquids if the mass flow rate is the same for the two holes? (b) what is the ratio rv1/rv2 of the volume flow rates from the two tanks? (c) at one instant, the liquid in tank 1 is 14.9 cm above the hole. if the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?

A0.750 kg aluminum pan is removed from the stove and plunged into a sink filled with 10.0 kg of water at 293 k. the water temperature quickly rises to 297 k. what was the initial temperature of the aluminum pan? the specific heat of aluminum is ca = 900 j/(kgk) and water is cw = 4190 j/(kgk)