Calculate the packing efficiency—the fraction of space that is filled—in the simple cubic and face-centered cubic crystal lattices. assume the spherical atoms are as big as they can be without overlapping one another. express your answers as percentages.

Two polarizers are oriented at 24.0∘ to one another. light polarized at a 12.0-degree angle to each polarizer passes through both. what is the transmitted intensity (%)?

Review multiple-concept example 7 in this chapter as an aid in solving this problem. in a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so that the ball in her hand moves in a circle. in one instance, the radius of the circle is 0.626 m. at one point on this circle, the ball has an angular acceleration of 66.1 rad/s2 and an angular speed of 12.6 rad/s. (a) find the magnitude of the total acceleration (centripetal plus tangential) of the ball. (b) determine the angle of the total acceleration relative to the radial direction.

What practical value did astronomy offer to ancient civilizations?