Đề thi thử tốt nghiệp THPT môn Tiếng Anh trường THPT Nguyễn Trãi Sở GD&ĐT Hà Nội năm 2025

Some people look at an equation and see a bunch of complicated numbers and symbols while others see beauty (I). Now, thanks to a new tool created at Carnegie Mellon University, anyone can now translate the abstractions of mathematics into beautiful and instructive illustrations (II). This exciting new tool is named Penrose after the mathematician Roger Penrose, who is famous for using diagrams and other drawings to communicate complicated mathematical ideas (III). Penrose enables users to create diagrams simply by typing mathematical expressions and letting the software do the drawing (IV).

Unlike a graphing calculator, these aren’t restricted to basic functions, but can be complex relationships from any area of mathematics. “Some mathematicians have a talent for drawing beautiful diagrams by hand, but they vanish as soon as the chalkboard is erased,” said Keenan Crane, an assistant professor of computer science and robotics. “We want to make this expressive power available to anyone.”

Diagrams are often underused in mathematical communication, since producing high-quality illustrations is beyond the skill of many researchers and requires a great deal of time and effort. Penrose addresses these challenges by letting diagram-drawing experts turn their knowledge about creating diagrams into computer codes so that other users can access this capability using familiar mathematical language and a computer. “We started off by asking: ‘How do people translate mathematical ideas into pictures in their head?’” said Katherine Ye, a Ph.D. student in the Computer Science Department who is involved in the development of Penrose. “The secret sauce of our system is to empower people to easily ‘explain’ this translation process to the computer, so the computer can do all the hard work of actually making the picture.”

Once the computer learns how the user wants to see a mathematical object visualized – a vector represented by a little arrow, for instance, or a point represented as a dot – it uses these rules to draw several candidate diagrams. Users can then select and edit the diagrams they want from a gallery of possibilities. A special, simple-to-learn programming language was also developed so that they can easily convey the ideas in their minds to the Penrose system, Crane said. "Mathematicians can get very picky about notations," he explained. "We let them define whatever notation they want, so they can express themselves naturally.

The researchers will present Penrose at the SIGGRAPH 2020 Conference on Computer Graphics and Interactive Techniques, which will be held this July. “Our vision is to be able to dust off an old math textbook from the library, drop it into the computer and get a beautifully illustrated book – that way more people understand,” Crane said, noting that Penrose is a first step toward this goal.

(Adapted from sciencedaily.com)

Vietnamese cultural identity is a rich and intricate tapestry that reflects the nation’s long and storied history. Rooted in over a thousand years of civilization, Vietnam’s cultural identity is a fusion of indigenous traditions and external influences, shaped by its geographical location and historical interactions.

First and foremost, at the heart of Vietnamese culture is a deep reverence for family and community. Confucian values emphasizing respect for elders, filial piety, and social harmony have played a pivotal role in shaping Vietnamese society. These values are reflected in the close-knit family structures, hierarchical relationships, and communal rituals that are integral to daily life.

Secondly, Vietnamese cuisine is celebrated worldwide for its exquisite flavors and diversity. With its emphasis on fresh ingredients, fragrant herbs, and balanced flavors, Vietnamese food tells a story of the country's agricultural heritage and regional variations. Iconic dishes like pho, banh mi, and spring rolls have become global favorites, representing the culinary artistry deeply ingrained in Vietnamese culture. Also, Vietnam's artistic expressions are equally captivating. Traditional art forms like water puppetry, silk painting, and folk music continue to thrive alongside contemporary artistic movements. Áo dài, a graceful traditional dress, exemplifies the fusion of elegance and modesty in Vietnamese fashion, symbolizing cultural pride and identity.

Today, in the face of modernization and globalization, Vietnamese cultural identity remains resilient. While adapting to the challenges of the 21st century, the Vietnamese people continue to honor their traditions, celebrate their unique cultural expressions, and pass on their heritage to future generations, ensuring that their cultural identity remains vibrant and enduring.

The future of electric vehicles (EVs) is promising as technological advancements and environmental concerns (24) ______. As governments worldwide implement stricter emissions regulations and offer incentives for EV adoption, manufacturers are investing heavily in research and development.

(25) ______, resulting in longer ranges and faster charging times. For instance, new solid-state batteries have the potential to enhance energy density and safety, making EVs more practical for everyday use.

Additionally, the rise of autonomous driving technology is set to revolutionize the way we interact with vehicles. Many electric models are now equipped with advanced driver-assistance systems (26) ______. Furthermore, the integration of smart technology allows for seamless connectivity, enabling drivers to monitor their vehicle's performance and locate charging stations through mobile apps.

As charging infrastructure continues to expand, (27) ______, the convenience of owning an EV is increasing. This transition to electric vehicles not only promises a reduction in carbon emissions but also fosters a cleaner, healthier environment. Overall, (28) ______ and sustainable transportation.

Solo Female Travelers Club - Global Greeter Network

Looking to enhance your travel experience with a local perspective? Join the Global Greeter Network, a service (29) ______ to connect travelers with friendly locals eager to (30) ______ you around. Whether you're (31) ______ in a guided tour, a scenic walk, or simply being dropped (32) ______ at a spot of interest, this program offering flexible options allows you to explore new destinations without the hassle of finding transportation. Perfect for solo female travelers wanting (33) ______ locals and like-minded explorers, the Global Greeter Network provides access to exclusive travel groups. Share experiences, make friends, and discover hidden gems. This service is designed for those eager to experience (34) ______ in a safe, comfortable way.

(Adapted from Solo Female Travelers)

Culture is the heart of every society, reflecting traditions, values, and creativity. By understanding different cultures, we enrich our perspectives and build connections with (35) ______. Whether through art, language, or celebrations, culture (36) ______ our identities and offers a window into the lives of others.

Why Embrace Cultural Diversity? Celebrate Differences: Every culture has unique traditions, from festivals and dances to foods and clothing. (37) ______ experiencing these, we gain a deeper appreciation of our global community.

Language as a Key: Learning even a few words in another language can open (38) ______ to new friendships and understanding.

Art & Music: Cultural (39) ______ in music, paintings, and performances are windows into a community’s history and values.

Get Involved! Attend local cultural festivals. Try traditional cuisines from around the world. (40) ______ art and films from different countries. Celebrating culture brings us closer together.