Suppose we are given the unit square A in the plane with corners (0; 0), (1; 0), (1; 1) and (0; 1). (a) Find a linear transformation T that sends A to the parallelogram B with corners (0; 0), (1; 2), (2; 2) and (1; 0). (b) Is the linear transformation T unique? Why or why not? (c) What linear transformation S, other than the identity, would send A to itself? (d) Is there a linear transformation whose overall e ect would be to send A to B and then translate B in the horizontal direction by one unit? Explain. (e) Find a linear transformation that will send A to a parallelogram C of area 4 while still keeping (0; 0) and (1; 0) as two of its corners. (f) What is the general formula for the linear transformation that sends A to a parallelogram of area k while still keeping (0; 0) and (1; 0) as two of its corners?

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

12

step-by-step explanation:

12 + 5 = 17

12x2=24

24-7=17

option b  

step-by-step explanation:

we know that

the distance from point n to lm in the figure is equal to the distance of the perpendicular line to lm that passes through the point n

so

the distance is equal to the segment no

> given problem

therefore

the distance from point n to lm is equal to