Components of the force in (x1, 2,3) is given by the vector f-fsuppose that you transform to a new set of orthogonal axes '2.f'3) at the same origin but rotated by +30° about the 3 axis. what are the direction cosines, i. e., the elements of the rotation matrix rz(+30), and label them clearly as done in class? a. b. using (a), what are the components of f in (r',23), .e., what are fi? can give magnitude.) show that they are equal. d. why must the magnitude of the forces (result in (c)) be equal? e. if fi 1, f2 -2, and fa 3 (in newtons), what is the vector f and its magnitude?

The percent efficiency of a machine can never be 100% (or greater), because in the real world some energy is always converted into a. heat b. work c. input force d. output force

Thomas his older brothers, who own a junk yard, on the weekends to earn extra money. he likes to them push broken-down cars to the back of the junk yard because it makes him feel strong. last saturday, they pushed three cars with different weights, and he noticed he used different amounts of force for each one. the cars were the following weights: white car: 2,700 kg red car: 1,500 kg blue car: 2,100 kg think about how much force is needed to move each car. which correctly lists the cars in order from the most to least amount of force needed to move them? a) white, blue, red b) blue, red, white c) red, white, blue d) white, red, blue

Aboy with a mass 25 kg climbs into a small tree. he sits on a branch that is 2.o m above to the ground. what is his gravitational potential energy above the ground?