What are modern database management system's applications?
This is a very broad question. Homework?
Modern DBMS all have 1) a data manipulation language (DML) and 2) data definition language DDL which defines the structures which hold the data (tables, etc). The DML may be a proprietary language, and most DBMS also allow the use of SQL (Standard query language). Each DBMS may have additional tools and utilities for export or import of data, performance tuning. Most have at least one method of communicating with other databases, incorporating various protocols. An example is ODBC, the Open Database Connectivity protocol. All databases have some method of creating forms and reports.