Given two displacement vectors A⃗ =(3.00iˆ−4.00jˆ+4.00kˆ)mA→=(3.00i^− 4.00j^+4.00k^)m and B⃗ =(2.00iˆ+3.00jˆ−7.00kˆ)mB→=(2.00i^+ 3.00j^−7.00k^)m, find the displacements and their magnitudes for (a) C⃗ =A⃗ +B⃗ C→=A→+B→ and (b) D⃗ =2A⃗ −B⃗ D→=2A→−B→.

8. why do radio telescopes convert radio waves (analog signals) to electrical (digital) signals for analysis? (hint: what did the article say about the advantages of digital signals? )

What are the phases shown in a and d called?

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)