M1 S2 Mini Lab

Find the sum of the following vectors: and =< ♦

Find the sum and difference of the following vectors:     a. <-4,6>+<5,0> b. <-7,5>0<-5,-9>

Loblolly is a built-in R dataset that that records the growth of Loblolly pine trees. We are interested in the height column of Loblolly. The values in the height column can be converted into a vector of name x by the assignment: x <- Loblolly$height We can see the values in x by typing x and Return or Enter. Remember x <- Loblolly$height After this assignment, we can see the first six values in x by typing head(x) and Return or Enter a. Give the R code to assign the values in in the height column of Loblolly to the vector named x. (Easy-see above) b. Calculate the interquartile range of x using the R, IQR() function. c. Calculate the sum of the squares of the values in x. d. Calculate the sample mean of x. e. Calculate the sample variance of x. f. Calculate the sample standard deviation of x. f. Using R, calculate a trimmed mean of x. [ h.Enter your R script in the box below.

Write the following equation using vectors and matrices   x + y = -z

resolve the vectors into components

4. Subtract the vectors shown. (blue - green)

Answer key is in square brackets.

List as many equal vectors as possible for the diagram below: A B D E с

Write the following equation using vectors and matrices   x + y = -z 4x = 3 -6x + 5y + z = 7

A person starts walking from home and walks: 2 miles East 2 miles Southeast 6 miles South 1 miles Southwest 4 miles East This person has walked a total of 15 miles Find the total displacement vector for this walk: 6.707 + 8.121 X Invalid notation. If this person walked straight home, they'd have to walk 10.53 miles

There are 200 Grade 12 students in a school. 85 of them take Calculus-Vectors. 95 took Advanced Functions during semester 1. 88 students take Data Management over the two semesters. There are 7 students who took all three courses. 53 took Calculus-Vectors and Advanced Functions. 10 took Calculus-Vectors and Data Management. 21 took Advanced Functions and Data Management Draw a Venn diagram to represent the case. How many students take only Calculus and Vectors? How many students take only one math course? How many students do not take any math courses? How many students take only two math courses? How many students take any combination of math courses?

Provide one application of the study of vectors to aviation.

4. Determine the resultant of each combination of vectors. a. 25 km/h north and 81 km/h east