Applications of Determinants

 Area of triangle

Area of triangle can be found using the concept of determinants when the vertices of the triangle are given.

Application of deteminants

 Volume of the Parallelepiped

The determinant gives the (signed) volume of the parallelepiped whose edges are the rows (or columns) of a matrix. The volume interpretation is often useful when computing multidimensional integrals ('change of variables'). It is also useful for understanding (or defining) the 'cross product' in physics or mechanics.

1.4 TENSES [ PAST / PRESENT / FUTUER PERFECT TENSE]

 1.4 TENSES [ PAST / PRESENT / FUTURE PERFECT TENSE]

Perfect verb tense is used to show an action that is completed and finished, or perfected. This tense is expressed by adding one of the auxiliary verbs — have, has, or had — to the past participle form of the main verb. 

PRESENT PERFECT [SUB + HAVE / HAS + M.V (past participle form)]

Eg. I have eaten already.

      she just has written a letter to her brother.

    The present perfect is used to indicate a link between the present and the past. the time of the action is before now but not specified, and we are often more interested in the result that in the action itself.

PAST PERFECT [SUB + HAD + M.V (past participle form)]

    The past perfect refers to a time earlier than before now. it is used to make it clear that one event happened before another in the past. it does not matter which event is mentioned first - the tense makes it clear which one happened first.

Eg. I had eaten when I arrived his home.

      she had written a letter to her brother before she went out.

FUTURE PERFECT [SUB + SHALL/WILL + HAVE + M.V (past participle form)]

    The future perfect tense refers to a completed action in the future. When we use this tense we are projecting ourselves forward into the future and looking back at an action that will be completed some time later than now. it is most often used with a time expression.

Eg. I will have eaten by this time next week.

      she will have written a letter to her brother before she goes out.

Basic Engineering Chemistry -I

                                                  Unit -II

                                         2.2 Nuclear  Chemistry

      Nuclear reactor:  Click the below link

                      https://youtu.be/1R3lvRgCPqU

       

               Engineering Chemistry - I

                                  Unit -I

              1.1 Technology of Water I

     Click on this ( E- Quiz) link below

                         https://forms.gle/7kLmAdqxNXg6d7nf8

How to read Newspaper

 

Find a comfortable place to read your paper. Coffee shops, outdoor seating at restaurants, or your own easy chair are great places to settle in and enjoy reading your chosen paper. If you take the train to work, you can also read it there, on your way.

Decide your reading purpose. If you’re reading relaxation or pleasure, then you’re approach might be less structured. If you’re looking for a specific topic or for reading practice, you’ll need to be more organized.

Decide where you want to begin. After you’ve gotten a sense of the overall paper, choose the section or article that has caught your attention, based on your reading purpose. You might choose a headline article on the front page, or you might skip to another section and begin reading sports. Use the table of contents as your guide.

Graphical Representation of complex numbers

 

Graphical Representation of complex numbers

Representation of a Complex Number

A complex number of the form z = a + ib can be represented on the argand plane by considering its coordinates as (Re(z), Im(z)) = (a, ib). An Argand plane or a complex plane is a Euclidean plane concerning complex numbers where the real part of a complex number “a” is represented on the X-axis and the imaginary part “ib” is represented on the Y-axis. The modulus of the complex number (r) is the distance of the complex number represented as a point in the argand plane (a, ib), i.e., the linear distance between the origin (0, 0) and the point (a, ib). 

r = √(a2 + b2)

The argument of the complex number is the angle in the anticlockwise direction made by the line joining the geometric representation of the complex number and the origin, with the positive x-axis.

Argz (θ) = tan−1(b/a)

Polar Form of a Complex Number

A complex number can also be represented and identified on the argand plane by using its polar form. To represent the complex number on the argand plane, the polar form makes use of the modulus and argument of the complex number. A complex number z = a + ib is expressed as z = r(cosθ + isinθ) in its polar form, where r is the modulus and θ is the argument of a complex number. Here, r is equal to √(a2 + b2), whereas θ is equal to tan-1(b/a).

Conjugate of a Complex Number

The conjugate of a complex number is another complex number that has the same real part as the original complex number, and the magnitude of the imaginary part is also the same but with the opposite sign. Two complex numbers are said to be each other’s conjugates if their sum and product are real numbers. 

• The conjugate of the complex number z = a + ib is z̅ = a − ib.

• Sum of a complex number and its conjugate = z + z̅ = (a + ib) + (a − ib) = 2a
• Product of a complex number and its conjugate = z × z̅ = (a + ib)×(a − ib)= a2+b2