The answer to book two of PEP seventh grade, 2-unit section a section B self check

The answer to book two of PEP seventh grade, 2-unit section a section B self check

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In the seventh grade of Dian Dian Dian Dian, the answer is unit 8,

At 4:30 p.m. flat 3A Renmin building. Read B bbacb read c Tom has a birthday party

Let a be a real matrix of order n, and prove that a is an orthogonal matrix if and only if (a α, a β) = (α, β) for any n-dimensional vector α, β

　　(α,β)=β^Tα,(Aα,Aβ)=β^TA^TAα
Obviously when a is an orthogonal matrix (a α, a β) = (α, β)
Conversely, let m = a ^ TA, m be a symmetric matrix
Let α = β = E_ I get m (I, I) = 1, where E_ I is the ith column of the unit matrix
For I ≠ J, let α = E_ i,β=e_ j. M (I, J) = 0, so m = I

To process a certain part, a processes one in 3 minutes, B processes one in 3.5 minutes and C processes one in 4 minutes. A total of 3650 parts are processed. How many parts are processed by three people?
It can't be solved by equation

Efficiency a: efficiency B: efficiency C
=1/3：1/3.5：1/4
=28：24：21
A = 3650 ÷ (28 + 24 + 21) × 28 = 1400
B = 1400 △ 28 × 24 = 1200
C = 1400 △ 28 × 21 = 1050

The solution of 1 / 6x + 1 / 12x + 1 / 7X + 5 + 1 / 2x + 4 = x

x/6+x/12+x/7+5+x/2+4=x
3x/4+x/7-x=-9
21x+4x-28x=-252
-3x=-252
x=84

Warehouse A stores 120 tons of grain, and warehouse B stores three fourths less than warehouse A. how many tons of grain does warehouse B store? (use the equation to do) speed

Set B warehouse x tons
X+120*3/4=120
X+90=120
X=30
There are 30 tons in warehouse B

First aid, come in. Solve the equation: 2x + y = 5 ① x + 2Y = 4 ②

2x+y=5①
x+2y=4②
① The solution is x = 2
Substituting ①, the solution is y = 1
So x = 2, y = 1

What are the integral parts of 33 * 333.33 and 33.333 * 33.333
Thinking

333.33*333.33=333.33*3*111.11=999.99*111.11=1000*111.11-0.01*111.11=111110-1.1111=111108.8889
So the integer part is 111108. And the next one is the first 1 / 100, so it's 1111

The sequence {an} is an equal ratio sequence, the number of items is even, and each item is positive. The sum of all items is four times of the sum of even items, and a2a4 = 9 (A3 + A4). How many items in the sequence {lgan} have the largest sum?
guocheng!

∵a2a4 = 9 (A3 + A4) ∵ the square of A3 = 9 (A3 + a3q) ∵ the square of A3 = 9A3 (1 + Q) ∵ A3 = 9 (1 + Q) ∵ A1 = 9 (1 + Q) / Q ^ 2, the sum of all terms is s = A1 / (1-Q), the sum of all even terms is s even = a1q / (1-Q ^ 2) ∵ A1 / (1-Q) = 4 × a1q / (1-Q ^ 2) ∵ A1 > 0 ∵ 1 / (1-Q) = 4 × Q / (1-Q ^ 2) ?

73+2(x-4)=81

73+2(x-4)=81
73+2x-8=81
2x=81-73+8
2x=16
x=8