Let be the linear transformation that first reflects points through the -axis and then then reflects points through the line . find the standard matrix for
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In the case above, the standard matrix A for T:
T= [0 1]
[-1 0]
What is linear transformation about?A linear transformation is known to be a kind of a function that exist from one vector point to another and it is one that often respects the linear) structure of all of vector space.
Note that in the linear transformation;
T: R² R²
T= (x, y), (-x, y)
Since:
(x,y) - (x,-y) - (y,-x)
A= [-1 0]
[0 1]
A= [-1 0] = A= [-x]
[0 1] [y]
Then [tex]T_{b}[/tex] is the reflection of (x- y); Since;
B = [0 1]
[1 0]
Then [tex]T_{B} (T_{a}(x) )[/tex] = [0 1] = A= [-x]
[0 1] [y]
= [-x]
[y]
Then: T: = [0 1] [x]
[0 1] [y]
Therefore, In the case above, the standard matrix A for T:
T= [0 1]
[-1 0]
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Related Questions
The circumference of a circle is 25.12 miles. What is the circle's diameter? C=25.12 mi Use 3.14 for pi
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and diameter=2r
in your case, the circumference is 25.12 miles, so we plug it in to the first formula:
25.12=2pi*r
12.56=3.14*r
4=r
and since 2r=diameter, the diameter is 8
how do you change 87/9 into a mixed number
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Which of the following statements contain a variable?all that apply
A.there are 60 second in a minute
B.he is year old
C.double the number of pages in the book
D.the age of my friend
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Gotta write more for the 20 characters limit
t=sqrt(2h-40t/g) I'm not sure where to even start on this one.
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The radius of a circle is 4 millimeters. What is the circle's circumference? r=4 mm Use 3.14 for .
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The circumference of the circle is: 25.12 mm.
The Circumference of a CircleCircumference of a circle = 2πrGiven:
radius of circle = 4 mm
π = 3.14
Required:
Circumference of the circle
Thus:
Circumference of the circle = 2×3.14×4
Circumference = 25.12 mm
Therefore, the circumference of the circle is: 25.12 mm.
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The correct answer is the circle's circumference is approximately 25.12 millimeters.
To find the circumference of a circle, one can use the formula:
[tex]\[ C = 2\pi r \][/tex]
where [tex]\( C \)[/tex] is the circumference, [tex]\( \pi \) (pi)[/tex] is a mathematical constant approximately equal to 3.14, and [tex]\( r \)[/tex] is the radius of the circle.
Given that the radius [tex]\( r \)[/tex] is 4 millimeters, we can substitute the values into the formula:
[tex]\[ C = 2 \times 3.14 \times 4 \text{ mm} \][/tex]
Now, we perform the multiplication:
[tex]\[ C = 2 \times 3.14 \times 4 = 25.12 \][/tex]
ten less than triple a number is 21
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Hope this helps
Janice has car insurance that she must pay four times a year. If each payment is $156, how much money should she set aside each month to cover her car insurance? $13 $26 $39 $52
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[tex]\left[\begin{array}{ccc}A&13&-\\B&26&-\\C&39&-\\D&52&Correct\end{array}\right][/tex]
A $65 coat is now on sale for $52. What percent discount is given?
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because if 65 is 100,
52 is 80% out of 65
so 100 - 80 is 20
What is the greatest fraction you can make using the digits 4, 7, and 9?
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Answer:
(7^9)/4 = 40,353,607/4
Step-by-step explanation:
Assuming each digit is used once and exponentiation is allowed, the largest numerator and smallest denominator will result in the largest fraction.
__
If other functions, such as factorial are allowed, then there might need to be a limit on the number of times they are applied. For example,
(7!)^(9!)/4 has about 1 million digits
something like ...
((7!)^(9!))!/4 has many more digits than that
and you can keep piling on the factorial symbols to any desired depth.
whats (-2,8) and (-22,8) finding the slope from points
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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 1515 in. by 99 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume.
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Please, see the attached files.
Thanks
you sure answer for number 9 to calculate how much money mr. and mrs. J make per week there 52 weeks per year the answer I came up with for the first one was $82,796
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How much do they make together? Correct answer equals - (42038.798) is how much money Mr. and Mrs. Jay make together!
Hope this helps.
Have a great day!
1,600 principal earning 7%, compounded annually, after 33 years
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It costs $7.00 to play a very simple game in which a dealer gives you one card from a deck of 52 cards. if the card is a heart, spade, or diamond, you lose. if the card is a club other than the queen of clubs, you win $11.50. if the card is the queen of clubs, you win $50.00. the random variable x represents your net gain from playing this game once, or your winnings minus the cost to play. what is the mean of x, rounded to the nearest penny?
a. $3.38
b. −$3.62
c. −$3.38
d. $3.62
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If the card is a heart, spade, or diamond, you lose.
If the card is a club other than the queen of clubs, you win $11.50.
If the card is the queen of clubs, you win $50.00.
The random variable x represents your net gain from playing this game once, or your winnings minus the cost to play. What is the mean of x, rounded to the nearest penny?
------
Random "winnings"::.....-7.......4.50......43
Probabilities::........ 39/52....12/52....1/52
------------------------------------------------------
u(x) = [39*-7 + 12*4.5 + 43]/52 = -$3.38
if you live 1 mile from work and can walk 4mph how long will it take you to get to work
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1 mile = 1/4 hour
1/4 hour = 15 mins
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Answer: It takes you 15 mins to walk to work
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what is the volume of a cube with a side length of 5/6 cm
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hope this helps! :)
you have a piggy bank containing a total of 93 coins in dimes and quarters. If the piggy bank contains $14.85, how many dimes are there in piggy bank
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Let q = number of quarters.
The total number of coins is 93, so the first equation is
d + q = 93
The value of 1 dime is $0.10. The value of 1 quarter is $0.25.
d dimes are worth 0.1d, and q quarters are worth 0.25q.
The total value of the coins is $14.85, so that gives us our second equation.
0.1d + 0.25q = 14.85
Now we have a system of two equations in two unknowns.
d + q = 93
0.1d + 0.25q = 14.85
Rewrite the first equation. Then multiply both sides of the second equation by -10, and write it underneath. Then add the equations.
d + q = 93
-d - 2.5q = -148.5
------------------------
-1.5q = -55.5
Divide both sides by -1.5.
q = 37
Now substitute 37 for q in the first original equation and solve for d.
d + q = 93
d + 37 = 93
Subtract 37 from both sides.
d = 56
Answer: There are 56 dimes in the piggy bank.
Draw three dimes 1 nickel and 2 pennies. Describe how to count on to find the total value of this group of coins
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The total value of this group of coins can be found by first counting the value of each type of coin, and then adding them all together. The value of a dime is 10 cents, so if there are three dimes, the total value is 30 cents. The value of a nickel is 5 cents, so if there is one nickel, the total value is 5 cents. The value of a penny is 1 cent so if there are two pennies, the total value is 2 cents. After adding 30 + 5 + 2, the total comes to $0.37.
Help me with this question pleaseeee!!!
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the measure of angle ∅=7*pi/6
the measure of its reference angle is?
remember that pi=180°
then
7*pi/6=7*180/6=210°------------> III Quadrant
Part A) its reference angle is 210°-180°=30°
Part B) sin(30°)=-0.5--------> negative because belongs III quadrant
The ratio of the areas of two similar polygons can be found by using the ratio of their perimeters or the ratio of similarity and squaring it. Always Sometimes Never
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The ratio of the areas of two similar polygons can be found by squaring the ratio of their perimeters or corresponding linear dimensions, but this method only works sometimes, specifically with similar polygons, and not with non-similar ones.
The ratio of the areas of two similar polygons is indeed found by taking the ratio of their corresponding linear dimensions and squaring it. This is because the area is a two-dimensional measurement, whereas perimeter and linear dimensions are one-dimensional. For similar polygons, which are polygons that have the same shape but may have different sizes, any linear dimensions (such as sides, perimeters, diagonals) are proportional.
When you have two similar polygons and you know the ratio of their perimeters, you can use this perimeter ratio to find the ratio of their corresponding side lengths since the ratio of the perimeters of similar polygons is equal to the ratio of their corresponding linear dimensions. After finding this linear ratio, you square it to obtain the ratio of their areas because if one dimension is multiplied by a scale factor 's', the area is multiplied by 's' squared (scale factor squared).
It is important to note, however, that this rule only applies to similar polygons (similarity) and not to polygons that aren't similar, since non-similar polygons do not have a constant ratio of corresponding linear dimensions. Therefore, to answer the original question, the method works sometimes, specifically when dealing with similar polygons.
A marker is randomly selected from a drawer that contains 20 green, 44 orange, and 30 blue markers.Which statement is true?
P(green)≈0.21P(blue)≈0.41P(orange)≈0.
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# green = 20
# orange = 44
# blue = 30
Total = 20 + 44 + 30 = 94
[tex]P(green) = \frac{20}{94} = 0.212 [/tex]
[tex]P(orange) = \frac{44}{94} = 0.468[/tex]
[tex]P(blue) = \frac{30}{94} = 0.319[/tex]
The one that matches is A
15+w+(-12)=15-12+w what is the answer
Answers
To solve this problem, we need to simplify.
15 + w - 12 = 15 - 12 + w
3 + w = 3 + w
w = w
So, the answer is undefined, since w is not given.
Hope this helps!
rose rode the roller coaster 9 times. Leila rode the roller 6 less times than Rose. Joseph rose roller coaster 5 times as many as Leila. how many times did Joseph ride the roller coaster?
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Because - 9 - 6 = 3 x 5 = 15
A brother and sister split the $990,000 from the sale of their parent's house. According to the will, the sister was to receive 25% more than her brother, for having managed the property. How much money did the sister receive?
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.. sister : brother = 1.25 : 1 = 5 : 4
Then the sister receives 5/(5+4) = 5/9 of the total, $550,000.
the answer ............
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g(0) = 2
1. f(g(0)) = f(2) = 0
2. h(f(0)) = h(2) = 2² -3 = 1
3. h(g(0) +1) = h(2 +1) = h(3) = 3² -3 = 6
CAN SOMEONE HELP PLZ AND EXPLAIN BEC IF DONT DO GOOD I CANT GO TO MY DADS HOUSE THIS WEEK END
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6.
Since the area is that of a square, you know that all side lengths are the same.
Area is base times height (A = bh), but since base and height are the same for a square, you get the formula A = a².
[tex]A = a^{2} [/tex]
[tex]144 = a^{2} [/tex]
[tex] \sqrt{144} = a[/tex]
[tex]12 = a[/tex]
The length of the side of a square with an area of 144 in² is 12 in.
7.
Rational number.
8.
This is a right triangle; use the Pythagorean Theorem to find missing lengths of right triangles. Pythagorean Theorem: a² + b² = c², where c is the hypotenuse of the triangle.
Plug in your leg lengths:
a² + b² = c²
8² + x² = 21²
64 + x² = 441
x² = 377
x = 19.4
Simplify. 7 to the second power + 3 (-9-7) + 88 divides by 8 + 3 to the second power
Answers
7[tex] x^{2} [/tex]+3 x - 16 + 88 ÷ 8 + [tex] 3^{2} [/tex]
49 + 3 x -16 + 88 ÷ 8 + [tex] 3^{2} [/tex]
49 + 3 x - 16 + 88 ÷ 8 + 9
49 - 48 + 88 ÷ 8 + 9
49 - 48 + 11 + 9
= 21
Your answer is 21.
Brainliest please?
If the Federal Reserve decreases the reserve rate from 5% to 2.5%, how does this affect the amount of money that would result because of fractional-reserve banking from an initial deposit into a bank of $35,000? A. It incraeses the amount by 1,400,000 B.It decreases the amount by 1,400,000 C.It decreases the amount by 700,000 D. It increases the amount by 700,000
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.. 35000/5% = 700,000
to
.. 35000/2.5% = 1,400,000.
It increases the amount by 700,000, corresponding to the 4th selection.
A trucker traveled an average of 48.6 miles each hour on a 583.2-mile trip. For how many hours did the trucker travel?
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Answer: The trucker traveled for 12 hours.
Step-by-step explanation:
Given : A trucker traveled an average of 48.6 miles each hour on a 583.2-mile trip.
i.e. Total distance = 583.2 miles
Average speed = 48.6 miles per hour
Using Formula , [tex]\text{Total Time}=\dfrac{\text{Total Distance}}{\text{Average speed}}[/tex]
We have
[tex]\text{Total Time}=\dfrac{583.2}{48.6}\\\\=\dfrac{5832}{486}\\\\=12\text{ hours}[/tex]
Hence, the trucker traveled for 12 hours.
because his goal is to bike 65 miles over the four days what equation can be used to find the number of miles he should bike on the first day
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Answer: 16.25
[tex]y = 65 \div 4[/tex]