What is the square of the identity matrix equal to?

What is the square of the identity matrix equal to?

Or identity matrix! The nth power of identity matrix is identity matrix (n ∈ n +)
The inverse of the identity matrix or the identity matrix!

Let a satisfy a square-a-4i = zero matrix, and prove that A-I, a-2i are invertible, where I is the identity matrix

A ^ 2-a-4i = 0, then there is a ^ 2-A = 4I, that is, (A-I) a = 4I, then (A-I) (1 / 4A) = I, so (A-I) is invertible and the inverse matrix of (A-I) is (1 / 4) A. from a ^ 2-a-4i = 0, a ^ 2-2a + a-2i = 2I, that is, (a-2i) a + (a-2i) = 2I, then (a-2i) [1 / 2 (a + I)] = I, so a-2i is invertible, and the inverse matrix of a-2i is 1 / 2 (a + I)

Fill in the blanks with the proper form of the English words given
We should practise_______ (read)English as_______ (more)as possible

we should practise reading English as much as possible
It's not countable to read English as a noun, so use much

Let the sum of the first n terms of the arithmetic sequence be Sn, if A1 = 0.5, S4 = 20, then S6 is

s4=(a1+a4)*4/2
=(2a1+3d)*2
20=(2*0.5+3d)*2
10=1+3d
d=3
s6=(a1+a6)*6/2
=(2a1+5d)*3
=(2*0.5+5*3)*3
=16*3
=48

Given a (- 3,4), B (5, - 2), then the module of vector ab=

Because we know a (- 3,4), B (5, - 2)
→ → →
So AB = B - A
→
AB=(8,-6)
Vector AB = B (5, - 2) - A (- 3,4) = (8, - 6) ---- the square root of vector AB = (8x8 + 6x6), that is, 10

How can you easily calculate the two problems of 5 / 6 minus 3 / 4 plus 1 / 3, 7 / 8 minus 5 / 12 plus 1 / 6?

Five sixths minus three fourths plus one third
=10 / 12 - 9 / 12 + 4 / 12
=5 out of 12
.
Seven eighths minus five twelfth plus one sixth
=7 out of 8 - (5 out of 12 - 2 out of 12)
=7 / 8 - 1 / 4
=7 / 8 - 2 / 8
=5 out of 8

Volume formula of cone

The volume formula of frustum: v = [S + s ′ + √ (SS ′)] h △ 3 = π H (R ^ 2 + R + R ^ 2) / 3
R - upper and lower radius
R - bottom radius
H-high

Does the differentiability of binary function mean that all partial derivatives of binary function exist?

Yes

What is the difference between properties and properties? Why is density a property of matter instead of a property?

Properties are possessed by all substances, while properties are possessed by all substances, but different substances have different properties
Density is a property of matter, but the density of different matter is generally different, so density is a property of matter, not a property

The content, understanding and formula of Newton's three laws
It's better to be more detailed. I'm rather stupid

Newton's three laws Newton's three laws are important laws in mechanics, which are the basis of studying classical mechanics. 1. Newton's first law content: any object keeps static or moving in a uniform straight line, until it is forced to change this state by the force of other objects, Therefore, the motion state of an object is determined by its motion speed. Without external force, its motion state will not change. This property of an object is called inertia. So Newton's first law is also called inertia law. The first law also clarifies the concept of force. It is clear that force is the interaction between objects, It is pointed out that force changes the motion state of an object. Because acceleration describes the change of the motion state of an object, force is related to acceleration rather than speed. In daily life, if we don't pay attention to this point, it is easy to produce illusion, In fact, it only holds in inertial reference frame. Therefore, whether Newton's first law holds or not is often regarded as the criterion of whether a reference frame is inertial reference frame. 2. Newton's second law content: when an object is subjected to combined external force, it will produce acceleration, and the direction of acceleration is the same as that of combined external force, The acceleration is directly proportional to the combined external force and inversely proportional to the inertial mass of the object. The second law quantitatively describes the effect of the force and quantifies the inertial mass of the object. It is vector and instantaneous. It should be emphasized that the combined external force on the object will produce acceleration, which may change the motion state or velocity of the object, However, this change is related to the motion state of the object itself. In vacuum, because there is no air resistance, all kinds of objects, regardless of their mass, have the same acceleration because they are only subject to gravity. Therefore, when making a free fall, in the same time interval, 3. Newton's third law: the force and reaction between two objects are equal in size and opposite in direction on the same straight line. Note: in order to change the motion state of an object, other objects must interact with it. The interaction between objects is reflected by force, and the force is mutual, There must be reaction when there is action. They act on the same straight line, equal in size and opposite in direction. In addition, it should be noted that: (1) there is no distinction between primary and secondary action and reaction. They occur and disappear at the same time. (2) the pair of forces act on different objects and cannot be offset. (3) the action and reaction must be forces of the same nature. (4) they have nothing to do with the reference system