Ineed solution for ashcroft and mermin problem 22.4.
polarization of the normal modes of a monatomic bravais lattice.
(a) show that if k lies along a 3-, 4- , or 6-fold axis, then one normal mode is polarized along k, and the other two are degenerate and polarized perpendicular to k.
(b) show that if k lies in a plane of mirror symmetry, then one normal mode has polarization perpendicular to k, and the other two have polarization vectors lying in the mirror plane.
(c) show that if the point k lies in a bragg plane that is parallel to a plane of mirror symmetry, then one normal mode is polarized perpendicular to the bragg plane, while the other two have polarizations lying in the plane. (note that in this case the modes cannot be strictly longitudinal and transverse unless k is perpendicular to the bragg plane.)
to answer these questions, one must note that any operation that leaves both k and the crystal invariant must transform one normal mode with wave vector k into another. in particular, the set of three orthogonal polarization vectors must be invariant under such operations. in applying this fact one must remember that that if two normal modes are degenerate, then any vector in the plane spanned by their polarization vectors is also a possible polarization vector.

Jason and mia are both running in a race. as they approach the finish line, you being the physicist that you are decide to time how long it takes them to reach the end of the race. when you start your stop watch (you can take this as time t = 0 s) you notice that mia is an unknown distance d ahead of jason and both are moving with the same initial velocity v_0. you also notice that jason is accelerating at a constant rate of a_j, while mia is deaccelerating at a constant rate of -a_m. jason and mia meet each other for the first time at time t = t_1. at this time (t = t_1) jason's velocity is two times that of mia's velocity, meaning v_j (t_1) = 2v_m (t_1). a) draw the position vs. time graph describing mia's and jason's motion from time t = 0 to time t = t_1. clearly label your axes and initial conditions on your graph. b) draw the velocity vs. time graph describing mia and jason's motion from time t = 0s to time t = t_1. clearly label your axes and initial conditions on your graph. c) how long from when the stop watch was started at t = 0s did it take mia and jason to meet? express your answer in terms of know quantities v_0, a_m, and a_j. d) when the stop watch started at time t = 0s, how far apart, d, were mia and jason? express your answer in terms of know quantities v_0, a_m, and a_j.

Which body part transports oxygen removes waste materials in carries nutrients to the body as part of the circulatory system

Complete these sentences. if a roller coaster train has a potential energy of 1,500 j and a kinetic energy of 500 j as it starts to travel downhill, its total energy isj. once the roller coaster train gets closer to the bottom of the hill, its kinetic energy increases to 1,100 j, and its potential energy decreases to j. when the train reaches the bottom of the track and is traveling along the ground, its kinetic energy isj.