Its All about Pj Problem Strings - 7 Spaces Of Interest and their associated Basic Sequences; 7 Pj Problems of Interest (PPI) and their Alleles (A)

WiseBites - Chew And Swallow

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I Charlie - A Farmer At Heart: From growing up on a farm in America to pioneering and working in Africa...more

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Selective Freedom: Freedom is the condition of not being controlled by another. The implication here is not that a person is ... more

Ultimate Reality: the awareness of being establishes reality ... more

Incidental Spying: Spying is incidental if the angle of reflection of the reflection of the incidental ray is zero (the incidental being is masked). When the incidental being is unmasked, the angle of incidence equals the angle of reflection and incidental spying becomes deliberate spying.

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Good Walls Bad Walls: A wall is a barrier that encloses a space. A wall does not have to be visible to the naked eye. The structure of a wall... more

Spying: spying is covert access into a space of interest in order to obtain data (measurement of observations) and information (shared knowledge). The spy (the entity spying)... more

Expressions Of Pj Problems

Pj Problems - Overview
7 Spaces Of Interest - Overview
Creation As Expresion Of Pj Problems
Survival As Expression Of Pj Problems
Energy As Expression Of Pj Problems
Language As Expression of Pj Problems
The Atom As Expression Of Pj Problems
Work As Expression Of Pj Problems
States Of Matter As Expressions Of Pj Problems
Nuclear Reactions As Expressions Of Pj Problems
Molecular Shapes As Expressions Of Pj Problems
Electron Configurations As Expressions Of Pj Problems
Chemical Bonds As Expressions Of Pj Problems
Energy Conversion As Expression Of Pj Problems
Chemical Reactions As Expressions Of Pj Problems
Electromagnetism As Expression Of Pj Problems
Continuity As Expression Of Pj Problems
Growth As Expression Of Pj Problems
Human-cells As Expressions Of Pj Problems
COHN - Nature's Engineering Of The Human Body
The Human-Body Systems As Expressions Of Pj Problems
Vision As Expression Of Pj Problems
Walking As Expression Of Pj Problems
Photosynthesis As Expressions Of Pj Problems
Systems As Expressions Of Pj Problems
Algorithms As Expressions Of Pj Problems
Networks As Expressions Of Pj Problems
Search As Expressions Of Pj Problems
Differential Calculus As Expression Of Pj Problems
Antiderivative As Expression Of Pj Problems
Integral Calculus As Expression Of Pj Problems
Inflation As Expression Of Pj Problems
Markets As Expressions Of Pj Problems
Money Supply As Expression Of Pj Problems
Painting As Expressions Of Pj Problems
Mind Warm Ups

The point "." is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

A = ((aij)), is the matrix
representing a a shear parallel to the x-axis.
a11 = 1; a12 = k; a21 = m; a22 = n.
A maps the vertices of a rectangle onto the vertices of a parallelogram as follows:
(0,0) -> (0,0); (2,0) -> (2,0);
(2,1) -> (5,1); (0,1) -> (3,1).
Determine the values k, m and n.

A = ((aij)), is a scalar transformation matrix of order 2.
a11 = k; a22 = 1/4.
Determine if A represents a uniform stretching of the plane or a uniform compression of the plane.
What change should be made in A inorder for it to represent a dilation of the plane.
What is the difference between a transformation matrix representing a dilation of the plane
and the transformation matrix representing a magnification of the plane.

The Linear Transformations T1 and T2 are reflections of the plane.
T1 is the case where the points on the x-axis are fixed points.
T2 is the case where the points on the y-axis are fixed points.
Determine the reflection matrix of:
(a)T1 (b)T2

((Aij)) and ((Bij)) are reflection matrices of reflections of the plane.
A11 = 0; A12 = 1; A21 = 1; A22= 0
B11 = 0; B12 = -1; B21 = -1; B22= 0
Determine: (a) The mirror associated with ((Aij))
(b) The mirror associated with ((Bij))

What is the determinant of the rotation matrix of the following transformation:
T(x, y) = (xcosθ - ysinθ, xsinθ + ycosθ).

What is the matrix of the transformation:
T(x, y) = (-x, -y)?

Identitfy the rigid motions that correspond to the following transformations:
(a) T(x, y) = (x+7, y-7).
(b) T1T2(x, y).
Where T1(x, y) = (x, -y) and T2(x, y) = (y, -x).
(c) T(x, y) = (xcosθ - ysinθ, xsinθ + ycosθ).

Abigail asked Abel to work on the transformation
T(x, y) = (x2, xy). Abel computed T and told Abigail he is not interested in T because it corresponds to a non-rigid motion. What is a non-rigid motion? Is Abel right? Describe the non-rigidity of T.

T is an identity transformation. Vector u = (x, y). What is T(u)?

T is a one-to-one linear transformation from the m-dimensional linear space X into the n-dimensional linear space Y. What is the value of m if n2 = 9?

Problems by Peter O. Sagay

What is Time?
St Augustine On Time
Bergson On Time
Heidegger On Time
Kant On Time
Sagay On Time
What is Space?
Newton On Space
Space Governance
Leaders
Imperfect Leaders
Essence Of Mathematics
Toolness Of Mathematics
The Number Line
Variables
Equations
Functions
The Windflower Saga
Who Am I?
Primordial Equilibrium
Primordial Care
Force Of Being
Forgiveness

Blessed are they that have not seen, and yet have believed. John 20:29

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