Three spin-1/2 particles are fixed in position on the vertices of an equilateral triangle. the interaction amongst themselves and with a uniform external magnetic field, b, is described by the hamiltonian where s, i 1,3, are spin operators, and a is a constant (in units of energy/12). (a) obtain the eigenvalues and eigenvectors of h (b) discuss the degeneracies of the spectrum when b-0. (c) discuss the nature of the ground state when a 0 and when a < 0, still for b 0. (d) discuss the effect the magnetic field causes to the degeneracies when it is switched on.

Ogle–2013–blg–0723 is an exoplanet that is similar to earth in size and proximity to its star. this exoplanet has mass m=4.18×1024kg and radius r=5.66×106m. an astronaut whose weight on earth is w=735n lands on the planet. a. calculate m, the mass of the astronaut. b. calculate gp? , the acceleration due to gravity on the surface of ogle–2013–blg–0723. c. calculate wp? , the weight of the astronaut on the surface of ogle–2013–blg–0723. d. calculate v, the minimum velocity required to put an object into orbit above ogle–2013–blg–0723. e. calculate t, the time required to complete an orbit around ogle–2013–blg–0723.

Crowbar of 5 metre is used to lift an object of 800 metre if the effort arm is 200cm calculate the force applied

Which of the following is the phase that results when the moon is on the opposite side of the earth from the sun? a. quarter moon b. crescent moon c. new moon d. full moon