*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*

**Spiritual** But Not **Religious** - Kimberlee J. Benart : I saw the title of the blog and took the time to read it, but how it saddened me to see it full of harsh unkindness ... more

**Mis-Information** As A **Weapon** - The Larger Issue: *Information* is *shared knowledge*. The knowledge shared does not have to be accurate...more

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

**One** Nation Under **What?**: A nation is a group of individuals with different identities... more

**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*.

**All** is Mathematics: *Nature only speaks mathematics* within the context of 7 universal concepts (Pj problems). This language is uniform everywhere in the Universe and is ... more

**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** = ((a_{ij})), is the matrix

representing a *a shear parallel to the x-axis*.

a_{11} = 1; a_{12} = k; a_{21} = m; a_{22} = 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** = ((a_{ij})), is a scalar transformation matrix of order 2.

a_{11} = k; a_{22} = 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 T_{1} and T_{2} are reflections of the plane.

T_{1} is the case where the points on the x-axis are fixed points.

T_{2} is the case where the points on the y-axis are fixed points.

Determine the reflection matrix of:

(a)T_{1} (b)T_{2}

((A_{ij})) and ((B_{ij})) are reflection matrices of reflections of the plane.

A_{11} = 0; A_{12} = 1; A_{21} = 1; A_{22}= 0

B_{11} = 0; B_{12} = -1; B_{21} = -1; B_{22}= 0

Determine: (a) The *mirror* associated with ((A_{ij}))

(b) The *mirror* associated with ((B_{ij}))

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) **T**_{1}**T**_{2}(x, y).

Where **T**_{1}(x, y) = (x, -y) and **T**_{2}(x, y) = (y, -x).

(c) **T**(x, y) = (xcosθ - ysinθ, xsinθ + ycosθ).

Abigail asked Abel to work on the transformation **T**(x, y) = (x^{2}, 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 n^{2} = 9?

*Problems by Peter O. Sagay*