What are natural magnets and why do they have magnetic properties?

 Natural magnets are permanent magnets found in the earth's crust, such as lodestone (a magnetized form of the iron oxide mineral magnetite). They form naturally when deposits are exposed to intense magnetic fields—like the Earth's magnetic field over long periods or powerful natural events like lightning strikes. 

Why They Have Magnetic Properties

Electron Spin: Every atom has electrons that spin and create tiny magnetic fields.
Unpaired Electrons: In most materials, these magnetic fields cancel each other out. In magnetic materials like iron, many electrons point in the same direction.
Magnetic Domains: Atoms group into tiny regions called domains.
Alignment: In a natural magnet, these domains point in one uniform direction, creating a strong overall magnetic force.

Electrons drift in a conductor from lower to higher potential, does this mean that all free electrons are moving in the same direction?

 

find value of a for which f(x) = x^2 -2ax + b f(x) is an increasing function for x>0

 

Determinant of a skew symmetric matrix

 

If A is a square matrix of order 3 such that det(A)=9, then det(9A^-1) is?

 

If A is a 3x3 matrix , B is a 3x1 matric and C is a 1x3 matric then only AB and BC are defined?

 The statement is false because, in addition to AB and BC, the matrix products AC and  CB are also perfectly well-defined. 

Conclusion

Apart from AB and BC, the products CB and CA are also defined. 

How can we build a chatting app like whatsapp that works on phone text messaging

To build a chat app like WhatsApp that runs on phone text messaging, you need to use an SMS Gateway API, set up a backend server, and create a mobile user interface. [1, 2]

Core Architecture & Tools

SMS Gateway API: Use services like Twilio or Vonage to send and receive real phone text messages (SMS) programmatically.
Backend Server: Build a server using Node.js or Erlang to process incoming and outgoing text logs.
Database: Store user phone numbers, message history, and profile data using databases like PostgreSQL, Firebase Firestore, or MongoDB.
Mobile Frontend: Develop cross-platform mobile screens using Flutter or React Native so the app works on both Android and iOS. [1, 2, 3, 4, 5]

Development Steps

User Verification: Implement phone number login by sending a random verification code via SMS.
Sync Contacts: Request permission to read the phone’s address book and match numbers registered in your database.
Message Routing: Connect your mobile app to the backend so that when a user hits send, the app triggers an API request to dispatch an SMS or sync through your server data pipeline