The vector matrix [-3,-5] is rotated at different angles. Match the angles of rotation to the vector matrices they produce.
![The Vector Matrix [-3,-5] Is Rotated At Different Angles. Match The Angles Of Rotation To The Vector](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/tMySVoBUEUqbZVHKCyZ5DytFmuUWzt64.png)
Answers
Answer: The above answer is correct.
Step-by-step explanation: I got this correct on Edmentum.
![The Vector Matrix [-3,-5] Is Rotated At Different Angles. Match The Angles Of Rotation To The Vector](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/2E2x9J0VzUM7EGclJCRwghpvzQotvBNl.png)
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[tex]A' = \left[\begin{array}{cc}5.830\\-0.098\end{array}\right][/tex], [tex]\theta = \frac{2\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}-5.657\\-1.414\end{array}\right][/tex], [tex]\theta = \frac{7\pi}{4}[/tex]
[tex]A' = \left[\begin{array}{cc}-2.83\\5.098\end{array}\right][/tex], [tex]\theta = \frac{4\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}5\\-3\end{array}\right][/tex], [tex]\theta = \frac{\pi}{2}[/tex]
This exercise consist in finding the resulting Vector Matrix for each Angle of Rotation and a given Vector Matrix. The result is found by multiplying the given Vector Matrix for a Rotation Matrix, defined below as follows:
[tex]A' = R\cdot A[/tex] (1)
Where:
[tex]A[/tex] - Given vector matrix.
[tex]R[/tex] - Rotation matrix.
[tex]A'[/tex] - Resulting vector matrix.
For 2-dimension Vector Matrices, The Rotation Matrix is defined by the following entity:
[tex]R = \left[\begin{array}{cc}\cos \theta&-\sin \theta\\\sin \theta&\cos \theta\\\end{array}\right][/tex] (2)
Where [tex]\theta[/tex] is the Angle of Rotation, in radians.
Let be [tex]A = \left[\begin{array}{cc}x\\y\end{array}\right][/tex], the resulting vector matrix is found by (1) and (2):
[tex]A' = \left[\begin{array}{cc}\cos \theta&-\sin \theta\\\sin \theta&\cos \theta\end{array}\right] \cdot \left[\begin{array}{cc}x\\y\end{array}\right][/tex]
[tex]A' = \left[\begin{array}{cc}x\cdot \cos \theta - y\cdot \sin \theta\\x\cdot \sin \theta +y\cdot \cos \theta \end{array}\right][/tex]
If we know that [tex]A = \left[\begin{array}{cc}-3\\-5\end{array}\right][/tex], then the resulting vector matrix for each angle is, respectively:
[tex]\theta = \frac{\pi}{4}[/tex]
[tex]A' = \left[\begin{array}{cc}1.414\\-5.657\end{array}\right][/tex]
[tex]\theta = \frac{\pi}{2}[/tex]
[tex]A' = \left[\begin{array}{cc}5\\-3\end{array}\right][/tex]
[tex]\theta = \frac{2\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}5.830\\-0.098\end{array}\right][/tex]
[tex]\theta = \frac{4\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}-2.83\\5.098\end{array}\right][/tex]
[tex]\theta = \frac{5\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}-5.83\\0.098\end{array}\right][/tex]
[tex]\theta = \frac{7\pi}{4}[/tex]
[tex]A' = \left[\begin{array}{cc}-5.657\\-1.414\end{array}\right][/tex]
Therefore, we have the following answers:
[tex]A' = \left[\begin{array}{cc}5.830\\-0.098\end{array}\right][/tex], [tex]\theta = \frac{2\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}-5.657\\-1.414\end{array}\right][/tex], [tex]\theta = \frac{7\pi}{4}[/tex]
[tex]A' = \left[\begin{array}{cc}-2.83\\5.098\end{array}\right][/tex], [tex]\theta = \frac{4\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}5\\-3\end{array}\right][/tex], [tex]\theta = \frac{\pi}{2}[/tex]
Related question: https://brainly.com/question/11815899
Related Questions
PLEASE HELP 20 POINTS
SHOW ALL WORK
Answers
Answer:
Steps below
Step-by-step explanation:
8) x = y²/2 2rcosΘ = r²sin²Θ 2cosΘ = rsin²Θ
r = 2cosΘ/sin²Θ = 2cotΘcscΘ
9) (x+2)²+y²=4 y= rsinΘ x=rcosΘ
(rcosΘ+2)²+y²sin²Θ = 4
r²cos²Θ+4rcosΘ+4+y²sin²Θ=4
r²(sin²Θ+cos²Θ)+4rcosΘ=0
r²+4rcosΘ=0 r+4cosΘ=0
r = - 4cosΘ
10) r = 2sinΘ r=2* y/r r²=2y x²+y²=2y
x² + (y²-2y+4) = 4 x²+(y-2)² = 4
11) r = 3tanΘsecΘ = 3* (y/x) * (r/x)
1 =3y/x²
x² = 3y 3y = x²
Find the distance between the points (-3, 4) and (-3, -5).
Answers
Answer:
[tex]\displaystyle d = 9[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (-3, 4)
Point (-3, -5)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(-3+3)^2+(-5 - 4)^2}[/tex][Distance] [√Radical] (Parenthesis) Add/Subtract: [tex]\displaystyle d = \sqrt{(0)^2+(-9)^2}[/tex][Distance] [√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{81}[/tex][Distance] [√Radical] Evaluate: [tex]\displaystyle d = 9[/tex]How many fluid ounces are in 4 quarts?
A. 16 fl. oz
B. 32 fl. oz
C. 64 fl. oz
D. 128 fl. oz
Answers
Answer:
D: 128 fl. oz
Step-by-step explanation:
1 quart is 32, to multiply by 4. :D
Answer:
hi your ans is d hope it helps please give brainliest
Step-by-step explanation:
Marta can pick 10 baskets of peaches in one hour. How long will it take her to pick 60 baskets of peaches?
Answers
Answer:
It will take her 6 hours for her to pick 60 baskets of peaches.
Step-by-step explanation:
Target buys pants for $6.42 and marks up the price for customers by 70%. How much do they sell pants for?
0.7\left(6.42\right)=\$4.490.7(6.42)=$4.49
$4.49 is not the correct answer. What is the mistake? Explain.
Answers
$6.42*.70=$4.49 this is the mark up
Now $6.42+$4.49=$10.91 for the sales price
So Target sells the plants for $10.91 to their customers.
You just forgot to add the initial price to the mark-up
Hope it helps.
A car la 160 inches long
A truck is 7percentage longer thanks they car
Answers
Answer:
171.2
Step-by-step explanation:
7% x 160 = 11.2
11.2 + 160 = 171.2
Josh build a tower using blocks that linked together. I notice that he had 36 block in 3/8 of his tower. Exactly how many blocks were in this entire tower?
A. 96
B. 60
C. 12
D. 13 1/2
Answers
Please Help, what is the answer
Answers
Answer:
The correct option is (2).
Step-by-step explanation:
We need to find the value of the given expression i.e.
[tex]\dfrac{(8x^6)^2}{(4x^2)^3}[/tex]
We can calculate it as follows :
[tex]\dfrac{(8x^6)^2}{(4x^2)^3}=\dfrac{8^2\times (x^6)^2}{(4)^3\times (x^2)^3}\\\\=\dfrac{x^{12}}{x^6}\\\\=x^6[/tex]
So, the final answer is x⁶. The correct option is (2).
you want your markup to be 35% of the final selling price. Your cost is $200. For what price should you sell the product
a. $235.00
b. $270.00
c. $279.00
d. $307.69
Answers
Multiply 35% by 200 and get 70
Add that 70 to 200 and you’ll get B which is 270
Solve the simultaneous equation
4x-y=9
2x-3y= -23
Answers
Answer:
x = 5
y = 11
Step-by-step explanation:
y = 4x - 9
2x -3(4x - 9) = -23
2x - 12x + 27 = -23
-10x = -23 -27
-10x = -50
minus cancels out
x = 5
y = 4(5) -9
y = 20 - 9
y = 11
Please help me if you can 10 points if you help
Answers
Answer:
C) 0%
Step-by-step explanation:
Let’s give the square sides equaling 4. The area would equal 16.
Decreasing the top by 75% would make it 1. Increasing the bottom by 75% makes it 7.
(1+7)/2=4
The height is still four so 4x4=16
No change in area.
Can someone help meee
Answers
Answer:
69
the measure of angle will
111 + AXB = 180
AXB = 180 - 111
AXB = 69
hope it helps
Answer:
angle AXB= 180-111=69°
Step-by-step explanation:
A commuter airline makes lattes in the galley and sells them to passengers. A regular latte contains a shot of espresso, 1 cup of 2% milk, steamed, and 0.5 cup of whipped cream. The low-fat latte contains a shot of espresso, 1.25 cups of skim milk, frothed, and no whipped cream. The plane begins its journey with 100 shots of espresso, 60 cups of skim milk, 60 cups of 2% milk, and 30 cups of whipped cream. The airline makes a profit of $1.58 on each regular latte and $1.65 on each low-fat latte. Assuming that all lattes that are made can be sold, what would be the ideal mix of regular and low-fat lattes to maximize the profit for the airline?
Answers
Answer:
To maximize profit, the amount of each type of coffees made are;
The number of regular latte made = 52 cups
The number of low-fat latte made = 48 cups
Step-by-step explanation:
The given parameters are;
The number of espresso in a regular latte = 1 shot
The number of cups of 2% milk in regular latte = 1 cup
The amount of whipped cream in a regular latte = 0.5 cup
The number of cups of skim milk in the low-fat latte = 1.25 cup
The number of espresso in a low-fat latte = 1 shot
The amount of whipped cream in a low-fat latte = 0 cup
The number of cups of espresso in the journey = 100 shots
The number of cups of skim milk in the journey = 60 cups
The number of cups of 2% milk in the journey = 60 cups
The amount of profit the airline makes on each regular latte = $1.58
The amount of profit the airline makes on each low-fat latte = $1.65
Let 'x' represent the number regular lattes made and let 'y' represent the number low-fat lattes made, we have;
x ≤ 30/0.5 = 60
x ≤ 60
y ≤ 60
y ≤ 60/1.25 = 48
∴ y ≤ 48
x + y ≤ 100
Therefore, the given that more profit is made from the sale of low-fat latte than for regular latte, the maximum number of low-fat latte should be made
Therefore, the number of low-fat latte made, y = 48
Therefore, the number of regular latte made, x ≤ 100 - 48 = 52
For maximum profit, the maximum number of low-fat latte, 'x', should be made
Therefore, x = 52
The ideal mix of regular and low-fat lattes to maximize profit is 52 cups of regular latte and 48 cups of low-fat latte
The sum of two numbers is 15 and their difference is 11.
What are the two numbers
Answers
Answer:
13 and 2
Step-by-step explanation:
x+y=15
x-y=11
2x=26
x=13
13+y=15
y=2
USE SYSTEMS OF EQUATIONS
HEY can You help me with this work pls i need help don't put random. if u don't know it pls guys.
Answers
1️⃣Remove parentheses
6a+6+3x-2+2a+4
2️⃣Collect like terms
(6a+2a)+(6-2+4)+3x
3️⃣Simplify
8a+8+3x
Answer: 8a+8+3x
QUESTION 21️⃣Remove parentheses.
-2z-3+4c+6y+y+3c
2️⃣Collect like terms.
-2z-3+(4c+3c)+(6y+y)
3️⃣Simplify
-2z-3+7c+7y
Answer: -2z-3+7c+7y
QUESTION 31️⃣Subtracting (7.8 - 5.1t) from (2.8 - 3.2t)
(2.8 - 3.2t) - (7.8 - 5.1t)
2️⃣Remove the parentheses.
2.8 - 3.2t - 7.8 + 5.1t
= 5.1t - 3.2t + 2.8 - 7.8 (we have now shown the difference in another way)
3️⃣Subtracting the like terms, will give:
1.9t - 5
4️⃣Recall
(2.8 - 3.2t) - (7.8 - 5.1t).
(-3.2t + 2.8) - (-5.1t + 7.8)
Answer:
a. (-3.2t + 2.8) - (-5.1t + 7.8)
b. 1.9t - 5
c. (-3.2t + 2.8) - (-5.1t + 7.8)
QUESTION 41️⃣Simplify
1/2p-(1/4p-4)
2️⃣Simplify
p2-(p/4-4)
3️⃣Simplify
p2-p/4+4
4️⃣Combine Terms
(p/2-p/4)+4
5️⃣Combine Terms
p/4+4
Answer: p/4+4
Done ✔
13 in = ___________ ft
Answers
Answer:
1.0833333 Feet
Hope this helps! If I could have brainliest im trying to level up.
Step-by-step explanation:
13 Inches =
1.0833333 Feet
(rounded to 8 digits)
In the parallelogram below,
y = [?]
5y-20
2y+25
PLEASE HELP
Answers
So 5y-20=2y+25
Solve for y
3y=45
y=15
The answer is y=15
I don’t understand I need help
Answers
Answer:
3/29
Step-by-step explanation:
area of total rectangle is 12x8 or 96 sq cm
area of shaded square is 9
96 - 9 = 87 sq cm, which is area of unshaded region
9 out of 87 is the probability of selecting a point in the shaded region, which simplifies to 3/29
Answer:
lol i see r o b l o x
Step-by-step explanation:
Rectangle = bxh
thats is 96
the we know that the square in the middle is 3x3x3x3 or 81
then subtract the two which is 15
Jacqueline drove 72 km on 6 L of gasoline. Which of the following equations can be used to find how far she can travel on a full tank of 50 L?
Answers
Answer:
600 km
Step-by-step explanation:
72 (km on 6 L of gasoline) / 6 (liters of gasoline) = 12 (km per liter)
50 (liters of gasoline) * 12 (km per liter) = 600 (km that Jacqueline can drive using 50L of gasoline)
I hope this helps :)
Answer:
600
Step-by-step explanation:
took the test
What does it mean to evaluate?
Answers
Answer:
Evaluate means to assess or determine something.
Step-by-step explanation:
Answer:
Means to simply solve, sometimes you may need to show your thinking, depending on the question.
Step-by-step explanation:
find the term to term rules for the following sequences. 28 25 22 19 16 .
Answers
Answer:
a) next one is previous one -3
b) next one is 3 times previous one
what's the domain and range
Answers
range: -infinite
pls answer I'll mark u brainliest urgent
Answers
Answer:
a = 110
Please mark as brainliest if answer right
Have a great day, be safe and healthy
Thank u
XD
Answer:
A=110
that is what I think
difference quotient for f (x) = 2x + 3 /5x
Answers
Answer:
1 and -0.6
Step-by-step explanation:
Joel had a coin collection. He had two hundred coins,
which were dimes and quarters. The total value of his
collection was worth $32.
Remember to define your variables.
Create 2 equations
(Each equation should have a "common theme" for
example in this problem one equation will be the the
total number of coins and the other will be the total
value of the coins)
The next step is to solve the problem. Remember to
think of the best method for problem solving
Answers
Answer:
Joel's coin collection had 120 dimes and 80 quarters.
Step-by-step explanation:
Given that Joel had a coin collection of two hundred coins, which were dimes and quarters, and the total value was worth $32, to determine how many coins of each type he had, the following equations must be performed:
0.25 - 0.10 = 0.15
200 x 0.10 = 20
32 - 20 = 12
12 / 0.15 = 80
200 - 80 = 120
(80 x 0.25) + (120 x 0.1) = X
20 + 12 = X
32 = X
Therefore, Joel's coin collection had 120 dimes and 80 quarters.
natasha has a sales job and receieves $60,440 as her annual pay plus commission. her company pays her a commision of 12% on her total sales if she makes sales of $70,000 in the first 3 months how much will she be paid for those 3 months?
Answers
Answer:
$68,840
Step-by-step explanation:
70,000*12%=8,400
8440+64,440=$68,840
What is the value of x in the following equation? 4(x-1) = 2(x +1)
Answers
If Robert buys a candy bar for 78 cents, how much
change does he get back from a one-dollar bill?
32 cents
23 cents
22 cents
33 cents
Answers
Explanation:
One dollar is 100 cents.
Your equation would be...
100 - 78 = 22 (your change)
Subtract the amount given by the total cost to get the change.
there are 60 minutes in a hour.how many minutes are there in 24 hours
Answers
There are 1440 minutes in 1 hour
Step-by-step explanation:
Since there are 60 minutes in 1 hour multiply 60 by 24, you get 1440.
Can y’all please help me out?
Answers
Answer:
19.5 degrees
Step-by-step explanation:
180 - (33.5 + 127) =
180 - 160.5 =
19.5
Hope that helps!