(3 points) Observe that H1 = √ 1 2 +1 +1 +1 −1 is an orthonormal basis. Note that H2 = 1 2 +1 +1 +1 +1 +1 −1 +1 −1 +1 +1 −1 −1 +1 −1 −1 +1 can be written as a block matrix as H2 = √ 1 2 H1 H1 H1 −H1 , and an 8-by-8 matrix H3 can be defined as H3 = √ 1 2 H2 H2 H2 −H2 . Show that H2 and H3 are each orthonormal bases. (Hint: To show that distinct columns c1 and c2 have zero dot product, consider cases. Are c1 and c2 both among the left half ? The right half ? One of each? Also, does the √ 2 matter for zero dot products? )

Julius sold five times as many computers as sam sold last year. in total, they sold 78 computers. how many computers did julius sell?

The graph and table shows the relationship between y, the number of words jean has typed for her essay and x, the number of minutes she has been typing on the computer. according to the line of best fit, about how many words will jean have typed when she completes 60 minutes of typing? 2,500 2,750 3,000 3,250

Have you ever been in the middle of telling a story and had to use hand gestures or even a drawing to make your point? in algebra, if we want to illustrate or visualize a key feature of a function, sometimes we have to write the function in a different form—such as a table, graph, or equation—to determine the specific key feature we’re looking for. think about interactions with others and situations you’ve come across in your own life. how have you had to adjust or change the way you represented something based on either the concept you were trying to describe or the person you were interacting with? explain how the complexity or layout of the concept required you to change your style or presentation, or how the person’s unique learning style affected the way you presented the information.