# Get help with transformation properties

Recent questions in Transformation properties
Transformation properties

### The graph $$\displaystyle{y}=-{2}{\left({\frac{{{3}}}{{{2}}}}-{e}^{{{3}-{x}}}\right)}$$ by: a) Performing the necessary algebra so that the function is in the proper form (i.e., the transformations are in the proper order). b) Listing the transformations in the order that they are to be applied. c) Marking the key point and horizontal asymptote.

Transformation properties

### To measure the speed of a current, scientists place a paddle wheel in the stream and observe the rate at which it rotates. If the paddle wheel has radius 0.20 m and rotates at 100 rpm, find the speed of the current in m/s.

Transformation properties

### The value of the operation [8]+[6] in $$\displaystyle{Z}_{{{12}}}$$ and to write the answer in the form [r] with $$\displaystyle{0}\leq{r}{<}{m}$$.

Transformation properties

### Let $$\left\{v_{1},\ v_{2}, \dots,\ v_{n}\right\}$$ be a basis for a vector space V. Prove that if a linear transformation $$\displaystyle{T}\ :\ {V}\rightarrow\ {V}$$ satisfies $$\displaystyle{T}{\left({v}_{{{1}}}\right)}={0}\ \text{for}\ {i}={1},\ {2},\dot{{s}},\ {n},$$ then T is the zero transformation. Getting Started: To prove that T is the zero transformation, you need to show that $$\displaystyle{T}{\left({v}\right)}={0}$$ for every vector v in V. (i) Let v be an arbitrary vector in V such that $$\displaystyle{v}={c}_{{{1}}}\ {v}_{{{1}}}\ +\ {c}_{{{2}}}\ {v}_{{{2}}}\ +\ \dot{{s}}\ +\ {c}_{{{n}}}\ {v}_{{{n}}}.$$ (ii) Use the definition and properties of linear transformations to rewrite $$\displaystyle{T}\ {\left({v}\right)}$$ as a linear combination of $$\displaystyle{T}\ {\left({v}_{{{1}}}\right)}$$. (iii) Use the fact that $$\displaystyle{T}\ {\left({v}_{{i}}\right)}={0}$$ to conclude that $$\displaystyle{T}\ {\left({v}\right)}={0}$$, making T the zero tranformation.

Transformation properties

Transformation properties

### Whether the function is a linear transformation or not. $$\displaystyle{T}\ :\ {R}^{{{2}}}\rightarrow{R}^{{{3}}},{T}{\left({x},{y}\right)}={\left(\sqrt{{{x}}},{x}{y},\sqrt{{{y}}}\right)}$$

Transformation properties

### To determine. The correct graph for the function $$g(x)=-\frac{1}{2}f(x)+1$$ is B

Transformation properties

### To prove: $$\displaystyle{\left[{a},\ {b}\right]}\ {>}\ {\left[{c},\ {d}\right]}\ \text{if and only if}\ {a}{b}{d}^{{2}}\ -\ {c}{d}{b}^{{{2}}}\ \in{D}^{+}$$. Given information: $$\displaystyle\text{Acoording to the definition of "greater than,"}\ {>}\ \text{is defined in Q by}\ {\left[{a},\ {b}\right]}\ {>}\ {\left[{c},\ {d}\right]}\ \text{if and only if}\ {\left[{a},\ {b}\right]}\ -\ {\left[{c},\ {d}\right]}\in{Q}^{{+}}$$

Transformation properties

### Important questions of Geometry for SSC CGL Tier I In my previous session, I have discussed some concepts related to triangles. Today I will discuss some important questions of Geometry which used to appear in SSC exams. Generally, questions asked from this section are based on properties of various shapes like lines, angles, triangles, rhombus, circles etc.

Transformation properties

### $$\displaystyle\text{Let A be an}\ {n}\ \times\ {n}\ \text{matrix and suppose that}\ {L}:{M}_{{\cap}}\ \rightarrow\ {M}_{{\cap}}\ \text{is defined by}{L}{\left({x}\right)}={A}{X},\text{for}\ {X}\in{M}_{{\cap}}.\text{Show that L is a linear transformation.}$$

Transformation properties

### To find: The linear transformation $$\displaystyle{\left({T}_{{2}}{T}_{{1}}\right)}{\left({v}\right)}$$ for an arbitrary vector v in V. The vectors $$\displaystyle{\left\lbrace{v}_{{1}},{v}_{{2}}\right\rbrace}$$ is vasis for the vector space V. Given: The linear transformation with satisfying equations $$\displaystyle{T}_{{{1}}}{\left({v}_{{1}}\right)}={3}{v}_{{{1}}}+{v}_{{{2}}},$$ $$\displaystyle{T}_{{{1}}}{\left({v}_{{1}}\right)}=-{3}{v}_{{{1}}}+{v}_{{{2}}},\ {T}_{{{2}}}{\left({v}_{{{1}}}\right)}=-{5}{v}_{{{2}}},$$ and $$\displaystyle{T}_{{{2}}}{\left({v}_{{2}}\right)}=-{v}_{{{1}}}+{6}{v}_{{{2}}}$$ are given as $$\displaystyle{T}_{{{1}}}\ :\ {V}\ \rightarrow{V}$$ and $$\displaystyle{T}_{{{2}}}\ :\ {V}\rightarrow{V}.$$

Transformation properties

### Prove that the metric area is defined as $$\displaystyle{P}\ {<}\ {x}_{{{1}}},\ {y}_{{{1}}}\ {>}\ {\quad\text{and}\quad}\ {Q}\ {<}\ {x}_{{{2}}},\ {y}_{{{2}}}\ {>}$$. If the proof of examples says that the first properties (positive definiteness and symmetry) are trivial. Prove the versatility of properties for a given space.

Transformation properties

### To show: $$\displaystyle{a}\ {<}\ {\frac{{{a}+{b}}}{{{2}}}}\ {<}\ {b}$$ Given information: a and b are real numbers.

Transformation properties

### Angles A and B are vertical angles. If $$\displaystyle{m}\angle{A}={104}∘$$ what is the $$m\angle B?$$ $$\displaystyle{m}\angle{B}=∘{d}{e}{g}{r}{e}{e}{s}$$

Transformation properties

### Whether T is a linear transformation, that is $$\displaystyle{T}:{C}^{{1}}{\left[-{1},{1}\right]}\rightarrow{R}^{{1}}$$ defined by $$\displaystyle{T}{\left({f}\right)}={f}'{\left({0}\right)}$$

Transformation properties

### Angles A and B are complementary. If $$\displaystyle{m}\angle{A}={27}∘$$, what is the $$m\angle B?$$ $$\displaystyle{m}\angle{B}= \circ {d}{e}{g}{r}{e}{e}{s}$$

Transformation properties

### Whether T is a linear transformation, that is $$\displaystyle{T}:{C}{\left[{0},{1}\right]}\rightarrow{C}{\left[{0},{1}\right]}$$ defined by $$\displaystyle{T}{\left({f}\right)}={g}$$, where $$\displaystyle{g{{\left({x}\right)}}}={e}^{{{x}}}{f{{\left({x}\right)}}}$$

Transformation properties

### Whether the function is a linear transformation or not. $$\displaystyle{T}\ :\ {R}^{{{2}}}\rightarrow{R}^{{{2}}},{T}{\left({x},{y}\right)}={\left({x},{y}^{{{2}}}\right)}$$

Transformation properties