The x vector component of a displacement vector r has a magnitude of 129 m and points along the negative x axis. The y vector component has a magnitude of 118 m and points along the negative y axis. Find (a) the magnitude and (b) direction of vector r. Specify the direction as a positive angle with respect to the negative x axis.

A75-hp (shaft output) motor that has an efficiency of 91.0 percent is worn out and is to be replaced by a high-efficiency motor that has an efficiency of 95.4 percent. the motor operates 4368 hours a year at a load factor of 0.75. taking the cost of electricity to be $0.12/kwh, determine the amount of energy and money saved as a result of installing the high-efficiency motor instead of the standard motor. also, determine the simple payback period if the pu