How is light refracted inside a crystal ball ?

Astronomers discover an exoplanet (a planet of a star other than the sun) that has an orbital period of 3.87 earth years in its circular orbit around its sun, which is a star with a measured mass of 3.59 x 1030 kg. find the radius of the exoplanet's orbit.

The scalar triple product computes the magnitude m of the moment of a force vector f about a specified line. it is m = (r × f) · n, where r is the position vector from the line to the point of application of the force and n is a unit vector in the direction of the line. use matlab to compute the magnitude m for the case where f = [12, −5, 4] n, r = [−3, 5, 2] m, and n = [6, 5, −7].

Six pendulums of mass mand length las shown are released from rest at the same angle theta from vertical. rank the pendulums according to the numberof complete cycles of motion each pendulum goes through perminute. a. l= 1m m=2kg b. l= 4m m=1 kg c. l= 2 m m= 2 kg d. l= 1 m m= 4 kg e. l= 2 m m = 4 kg f. l= 4m m = 4kg