(Show work in a clear and logical manner +10) A yo-yo at rest starts rolling downhill without slipping from a height of [h] m measured from the foot of the hill.  What is the velocity of its center of mass when it reaches the foot of the hill? The yo-yo has a moment of inertial about its center as [I] kgm2, mass [M] kg, and radius [R] m. (Show work clearly with all steps). 1) What is the initial potential energy of the Yo-yo? 2) What is the velocity of its center of mass when it reaches the foot of the hill?  Enter the vcm rounded off to TWO decimal places.  

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(show work +15) Let’s suppose SpaceX is planning to release a 2-kg Starlink communication satellite to orbit Mars at an altitude of h=[h] km from the surface of Mars. Mass of Mars = 6.39 x 1023 kg, Radius of Mars  = 3390 km. a) What is the velocity of the satellite in that orbit?  b) What is the kinetic energy of the satellite? c) What is the potential energy of the satellite? d) What is the period of the satellite in that orbit around Mars?    Below, enter the answer to part d) the time in hours rounded off to TWO decimal places.    

The absorption spectrum of an unknown substance is shown below. What type of EM radiation is mostly absorbed by this substance? Picture5(1).png   

Find the minimum cost spanning tree on the graph above using Kruskal’s algorithm.  Which of the edges are included in the minimum cost tree?

What is the degree of vertex F? _______

This graph has a Hamiltonian Circuit.

Apply the sorted edges algorithm to the graph above.  Give your answer as a list of vertices, starting and ending at vertex A. _______

This essay question has two parts: 1. Based on research over the years and the information we covered in class, what are some qualities and attributes that would enable a person to be an effective therapist, whether at the master’s or doctoral level? In addition to the secular research on this topic, what would prayer, faith, and virtue also add to this discussion (as covered in Dr. Link’s opinion slide). If you want to be an effective therapist, what might be some things to avoid or try to minimize that you learned from our discussions as well as from the APA Code of Ethics.  2. Furthermore, research consistently demonstrates that the most curative factor in therapy is the therapeutic alliance. Talk about what you perceive the therapeutic alliance to be. What is it? Is it just a relationship or a paid friendship? What factors can be nurtured to make this relationship most effective? Do techniques or evidence-based practices even really matter?