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2 years ago

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Parallelogram PQRS is rotated 90° clockwise about the origin to create parallelogram P'QʻR'S'. Which rule describes this transfo

rmation? (Please leave a small explanation)

1 answer:

White raven [17]2 years ago

6 0

The answer would be H, because it is rotating 90 degrees which would end up on Quadrant l (+, +).
therefore your answer is H. If you need a little more explaining comment:))

You might be interested in

Evacuate 3 1.5 + 2 2.3

zaharov [31]

Answer:

53.8

Step-by-step explanation:

31.5 + 22.3

53.8

Hope it helps

3 0

2 years ago

Read 2 more answers

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + xzj + (x

Lady_Fox [76]

By Stokes' theorem, the line integral of $\vec F$ over $C$ is given by the surface integral of the curl of $\vec F$ over $S$ , where $S$ is the region of intersection of the plane $z=y+6$ and the cylinder $x^2+y^2=1$ with $S$ having positive/upward orientation.

Parameterize $S$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(u\sin v+6)\,\vec k$

with $0\le u\le1$ and $0\le v\le2\pi$ .

Take the normal vector to $S$ to be

$\vec s_u\times\vec s_v=-u\,\vec\jmath+u\,\vec k$

The curl of $\vec F$ is

$\nabla\times\vec F(x,y,z)=(1-x)\,\vec\imath-\vec\jmath+(z-2)\,\vec k$

Then the line integral is equivalent to

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{2\pi}\int_0^1\bigg((1-u\cos v)\,\vec\imath-\vec\jmath+(u\sin v+4)\,\vec k\bigg)\cdot\bigg(-u\,\vec\jmath+u\,\vec k\bigg)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^1(5u+u^2\sin v)\,\mathrm du\,\mathrm dv=\boxed{5\pi}$

4 0

2 years ago

Leon has 3/8 the number of tropical fish that haru has how many times the number of tropical fish Leon has is the number of trop

stealth61 [152]

Let
Haru's number ---> x
<span>Leon's number ---> (3/8)x
</span>so
ratio of
<span>Leon : Haru = (3/8)x : x </span>
<span>= 3/8 : 1 </span>
<span>= 3 : 8
</span>
the answer is
3 : 8

5 0

2 years ago

Read 2 more answers

What is the median of the data set below? 57, 21, 11, 35, 43, 19

Naily [24]

Answer:

28

Step-by-step explanation:

Arranged it in order and got 28 :)

8 0

2 years ago

Read 2 more answers

Could someone help me, please?

k0ka [10]

We can rewrite the expression under the radical as

$\dfrac{81}{16}a^8b^{12}c^{16}=\left(\dfrac32a^2b^3c^4\right)^4$

then taking the fourth root, we get

$\sqrt[4]{\left(\dfrac32a^2b^3c^4\right)^4}=\left|\dfrac32a^2b^3c^4\right|$

Why the absolute value? It's for the same reason that

$\sqrt{x^2}=|x|$

since both $(-x)^2$ and $x^2$ return the same number $x^2$ , and $|x|$ captures both possibilities. From here, we have

$\left|\dfrac32a^2b^3c^4\right|=\left|\dfrac32\right|\left|a^2\right|\left|b^3\right|\left|c^4\right|$

The absolute values disappear on all but the $b$ term because all of $\dfrac32$ , $a^2$ and $c^4$ are positive, while $b^3$ could potentially be negative. So we end up with

$\dfrac32a^2\left|b^3\right|c^4=\dfrac32a^2|b|^3c^4$

3 0

3 years ago