Problem 1- find the root locus of the following transfer functions by Matlab Hint copy the root locus figures you find in Matlab and paste all four on a word document, create a PdF from the Word file and upload on canvas): 5 1. H(s) = 2s+1 2. H(s): = 2 100 s²+10s+100 1000 3. H(s) = (s+5)(s²+68+25) 10000 4. H(s) = (s²+48+16) (s²+68+25)

(Dynamic Programming.) Recall the problem presented in Assign- ment 3 where given a list L of n ordered integers you're tasked with removing m of them such that the distance between the closest two remaining integers is maxi- mized. See Assignment 1 for further clarification and examples. As it turns out there is no (known) greedy algorithm to solve this problem. However, there is a dynamic programming solution. Devise a dynamic programming solution which determines the maximum distance between the closest two points after removing m numbers. Note, it doesn't need to return the resulting list itself. Hint 1: Your sub-problems should be of the form S(i, j), where S(i, j) returns the maximum distance of the closest two numbers when only considering removing j of the first i numbers in L. As an example if L [3, 4, 6, 8, 9, 12, 13, 15], then S(4, 1) = 2, since the closest two values of L' = [3,4,6,8] are 6 and 8 after removing 4 (note, 8-6 = = 2). = Hint 2: For the sub-problem S(i, j),…