Nagpur

Sana Begum replied | 2 days ago

create a structured routine by setting specific study times, organizing your workspace, and using a calendar to manage deadlines.

Lokesh replied | 6 days ago

A vector space is a collection (set) of things called vectors, where you can:

1. Add two vectors → result is still a vector (in the same set)

2. Multiply a vector by a scalar (a number) → result is still a vector (in the same set)

Basically, it’s a system where vector addition and scalar multiplication make sense and follow certain rules.

Pulkit Verma replied | 4 days ago

A vector space $V$V over a field $F$F (like $\mathbb{R}$R, $\mathbb{C}$C, or $\mathbb{Q}$Q) is a set equipped with two operations:

1. Vector addition: $+:V\times V\to V$+:V×V→V
   (You can add two vectors and get another vector.)

2. Scalar multiplication: $\cdot :F\times V\to V$⋅:F×V→V
   (You can multiply a vector by a scalar from the field.)

Saurabh Verma replied | 5 days ago

Articulation in music means how you play each note — whether it’s smooth, short, or strong.

Here are some simple examples:

Staccato (•) → Play the note short and jumpy.

Legato (curved line) → Play smoothly, join one note to the next.

Accent ( > ) → Play the note louder or stronger.

Tenuto (–) → Hold the note for its full time, a bit gentle.

Marcato ( ^ ) → Play the note very strong and bold.

🎹 In short way:

Articulation shows how to touch or press the keys — softly, sharply, or smoothly — to make the music sound more expressive.

Saurabh Verma replied | 5 days ago

Articulation in music means how you play each note — whether it’s smooth, short, or strong.

Here are some simple examples:

Staccato (•) → Play the note short and jumpy.

Legato (curved line) → Play smoothly, join one note to the next.

Accent ( > ) → Play the note louder or stronger.

Tenuto (–) → Hold the note for its full time, a bit gentle.

Marcato ( ^ ) → Play the note very strong and bold.

🎹 In short way:
Articulation shows how to touch or press the keys — softly, sharply, or smoothly — to make the music sound more expressive.