Let \(f\) be the transformation of \(\mathbb{R}^{2}\) given…

Let \(f\) be the transformation of \(\mathbb{R}^{2}\) given by rotating \(80^{\circ}\) counterclockwise around the origin. Find the standard matrix for \(f\) and then use that to find where the point \(\left(5,4\right)\) gets sent under this rotation. (As \(80^{\circ}\) is not a special angle, you will have to use decimal approximations.)

You recently learned about Mentors for Majors, a campus serv…

You recently learned about Mentors for Majors, a campus service program that pairs students with mentors. Mentors are alumni or other working professionals who have agreed to field student inquiries about the nature of their jobs and strategies for career success.  You’ve been thinking about a career and would like to get more information about it from an experienced professional.  Checking over the list, you find that there’s a mentor in your area.  Write an email to the person in which you ask questions about this field of interest. Show consideration for the reader and demonstrate your own serious interest in that type of career. End the email with an ask to meet up face-to-face to talk directly about his/her career.

You are preparing an in-person presentation to give to the c…

You are preparing an in-person presentation to give to the company’s board of directors as part of your internship.  Provide two or three strategies that you will use to ensure your audience is engaged.  What different strategies would you use if the presentation were online, through Zoom or Teams?