Consider the s- operator (the spin operator in the z-direction), and the sy operator (the spin operator in the y-direction). a. in the z-basis: i. what is s, in matrix format? what is the z+ state in matrix format? show that z+ state is an eigenvector of sz. what is the eigenvalue? iii. what is sy in matrix format? iv. what is the y+ state in matrix format? show that y+ state is an eigenvector of sy. what is the eigenvalue? v. show that z+ state is not an eigenvector of sy. vi. show that y+ state is not an eigenvector of sz. b. in the y-basis: i. what is sy in matrix format? ii. what is the y+ state in matrix format? show that y+ state is an eigenvector of sy. what is the eigenvalue? is the y+ state in the y-basis, the same state as the y+ state in the z-basis? explain. iv. is the sy operator in the y-basis, the same state as the sy operator in the z-basis? explain.

Aprojectile is launched horizontally 10m above the ground and with an initial velocity of 15 m/s. a) determine the magnitude and direction of projectile velocity at t= 1.3s b) determine the magnitude and direction of projectile acceleration at t=1.3s

Use the frequency histogram to complete the following parts. ​(a) identify the class with the​ greatest, and the class with the​ least, relative frequency. ​(b) estimate the greatest and least relative frequencies. ​(c) describe any patterns with the data. female fibula lengths 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 0 0.05 0.1 0.15 0.2 0.25 length (in centimeters) relative frequency a histogram titled "female fibula lengths" has a horizontal axis labeled "length in centimeters" from 30.5 to 39.5 in increments of 1 and a vertical axis labeled "relative frequency" from 0 to 0.25 in increments of 0.05. the histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. the approximate heights of the vertical bars are listed as follows, where the label is listed first and the approximate height is listed second: 30.5, 0.02; 31.5, 0.04; 32.5, 0.05; 33.5, 0.13; 34.5, 0.22; 35.5, 0.25; 36.5, 0.13; 37.5, 0.06; 38.5, 0.09; 39.5, 0.01. ​(a) the class with the greatest relative frequency is nothing to nothing centimeters. ​(type integers or decimals. do not round. use ascending​ order.)

Consider a one meter long horizontal pipe with a constant 100 cm^2 cross sectional area. water flows rightward into the pipe at x = 0 with flow velocity 02m/sec at every point within the pipe intake area. at x=1, the rightward flow rate is 0.192 m/sec. assume the water is a conserved quantity in the pipe, so there must be a leak (a sink) somewhere in the pipe. 1. compute net volumetric flow of the source if the system to be in equilibrium. 2. now assume the pipe in the problem has no leaks. compute the net volumetric rate of change for the system.